Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Trapezoidal Rule with h=0.05.

Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: Given integral is ∫03 x3+xdx Number of sub-intervals = 6 Take f(x) = x3+x Step size  ∆x  = 3-06…

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x) dx.

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Q: Evaluate the integral. (Use C for the constant of integration.) 13 tan (x) sec (x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 6 tan(x) sec³(x) dx

A: We have to find

Q: Evaluate the integral ,(1 – x – 4x³ + 2x³) dx a) Analytically b) Single application of trapezoidal…

A: we have  f(x)=1-x-4x3+2x5 we need to find ∫-24f(x)dx  a) analytically b) using trapezoidal rule

Q: Use integration by parts to find the indefinite integral.

A: We have to evaluate the following integral: int x2 ex/2 dx ; using integration by parts

Q: Use integration by parts to find the indefinite integral ∫x e1-x dx

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Q: |x| dx 1 X V1– x² -1

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Q: Evaluate the integral. (Use C for the constant of integration.) tan3(x) sec (x) dx

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Q: Evaluate the integral in terms of Beta function: ∫x^12(1−x)^16 dx    limit: 0 to 1

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Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x3 +x)dx

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Q: Use double integral to find the average temperature of T(x. y) = 10-8r -2y

A: Temperature function is given as - Tx, y = 10-8x2-2y2Average temperature = ∬10-8x2-2y2dxdyGiven…

Q: Use the tabular method to find the indefinite integral. ∫x3 cos 2x dx

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Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx

A: We need to use the mid-point rule to find the value of the definite integral.  The mid-point rule…

Q: Use the tabular method to find the indefinite integral. (Use C for the constant of integration.) (x…

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Q: Find the inde finite integral. (Use C for the constant of integration.) -5 dx (x2 + + 5)3/2

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Q: Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx 0,

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Q: Approximate the integral to three decimal places using the indicated rule. 308 -dx; trapezoidal…

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Q: Use the Trapezoidal Rule to evaluate the integral [x-'dx. .-1 1

A: Equation is f(x)=1xThe value of the table for x and y x 1 1.25 1.5 1.75 2 y 1 0.8 0.6667 0.5714…

Q: Find the general indefinite integral. (Use C for the constant of integration.) x' dx

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Q: Evaluate the integrals using integration by parts. ∫ x sin x cos x dx

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Q: Use the tabular method to find the integral. (Use C for the constant of integration.) 3x3 sin(x) dx

A: The given integral is ∫3x3sin x dx. ∫3x3sin x dx=3∫x3 sin x dx ddxxn=nxn-1∫sin xdx=-cos x+C∫cos…

Q: Evaluate the integral. (Use C for the constant of integration.) 4 tan(x) sec (x) dx

A: Given the integral, ∫4tan(x)sec3(x) dx = I(Say) Now, I=∫4tan(x)Sec(x)sec2(x) dx.........(1)  Now…

Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan (x) sec®(x) dx C must be in…

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Q: Evaluate the integral. (Use C for the constant of integration.) (arctan(x))5 | x2 + 1 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 11 tan“(x) sec (x) dx

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Q: Use Trapezoidal Rule with (n- 4) to find the integral dx x-1

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Q: Evaluate the integral. (Use C for the constant of integration.) (tan²(x) tan^(x) dx

A: Given       I=∫7tan2x++tan4xdx      = 7∫tan2x1+tan2xdx      = 7∫tan2x.sec2x dx∵sec2x-tan2x=1

Q: Use a table of integrals to find the length of the curve y = x² from x = 0 to x = 2. %3D

A: The equation of the curve is given as, y = x2 we need to find the length of curve in the interval x…

Q: Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

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Q: Evaluate the integral. (Use C for the constant of integration.) х dx x2 + x + 3

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Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan*(x) sec (x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) cos7(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) sec (x) dx

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Q: Evaluate the integral by u-substitution. (Use C for the constant of integration.) Integral of…

A: Given : Integral ∫Sin3(x) cos(x) dx   To find : Evaluate the integral by u-substitution?

Q: dx is: value of the integral sinx the Using Simpson's rule 113,

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 tan3(x) sec(x) dx

A: Let sec(x)=t sec(x)tan(x)dx=dt tan2(x)=sec2(x)-1 Substituting we get 2 int (t2-1)dt =2 (t3-t)+C…

Q: Evaluate the integral. (Use C for the constant of integration.) ] = 5 tan(x) sec³(x) dx

A: The given integration is: ∫5tanxsec3xdx To find the value of integration.

Q: f(x)=sin(x)/x_between 0 and 1 using Trapezoidal

A: fx=sinxx Trapezoidal rule fx≈h2fa+2fa+h+fa+2h+---+fb a=0, h=0.05 and b=1

Q: Evaluate the integral. (Use C for the constant of integration.) 8 tan(x) sec³(x) dx

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Q: 2. Use the composite trapezoidal rule to estimate the integral of y = sin(x) %3| from x = 0 to 2.…

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Q: 2. Estimate the integral using Simpson's approximation rule with n=4: sin t dt

A: To estimate:∫0πsint dtn=4

Q: Evaluate the integral. (Use C for the constant of integration.) ∫ 3 tan2(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 tan(x)sec^3(x)dx

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Q: Evaluate the integral. (Use C for the constant of integration.) | tan (x) sec(x) dx

A: Consider the integral ∫tan3xsecxdx

Q: 3. Estimate the value of the integral 1 dx (n = 4) using Trapezoidal rule. 1+ln x

A: The value of h in the trapezoidal rule is h = b-anh = 5-34h = 24h = 0.5 Form a table with the x…

Q: sin'(x) cos(x) dx

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Q: Use the Trapezoidal rule to approximate the integral from upper limit 1.05 to lower limit 1 e^-2x^2…

A: To find- Use the Trapezoidal rule to approximate the integral ∫11.05e-2x2 dx. Find an upper bound…