Factor x* + 1 as a difference of squares by first adding and subtracting the same quantity. Use this factorization to evaluate / 1/ | 1/ (x *+ 1) dx.

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

A:

Q: 2 * (1+x²)?" -00

A: Answer

Q: How much work is required to pump all the water from a right circular cylindrical tank that is 8…

A: How much work is required to pump all the water from a right circular cylindrical tank that is 8…

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: Use Secant Method to find the root of x³ + 3x² – 1= 0 between [-3, -2] accurate to five decimal…

A:

Q: Integrate the square root of (1 - sin² x) dx.

A:

Q: Find the second derivative of 1/square root of 2t

A:

Q: Use differentials to approximate the cube root of 0.009.

A: Approximate  0.00913

Q: 4. fx(1-x) dx

A: We can find the integration as below.

Q: . Estimate dx with an error less than 10-3.

A: Series sum estimation:

Q: Wt-1+2 dt

A: We will find the integral as following.

Q: Use the tabular method to find the indefinite integra. ∫x2(x − 2)32 dx

A:

Q: /8.9

A: Given : 8.93

Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: Verify the formulas by differentiation. ∫ (3x + 5)-2 dx = -(3x + 5)-1/3 + C

A: Given ∫(3x+5)-2dx=-(3x+5)-13+C Verify the formula by differentiation Consider Right hand side value…

Q: Find indefinite integral.

A: Let the given integral be y - y = ∫x12+3x-23 dx      Identity to be used - ∫xndx = xn+1n+1+C

Q: find integral sqrt (1 - 4x 2 ) dx

A:

Q: Use Secant Method to find the root of x³ + 3x² – 1= 0 between [-3, -2] accurate to five decimal…

A: We have f(x) = x3+3x2-1 f(-2) = -23+3-22-1 = 3 x1 = -2 f-3 = -33+3-32-1 = -1 x0 = -3

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

A:

Q: Calculate the root of the equation given as f(x) - x3 + 3x - 5 with the Regula-Falsi method in the…

A: Let  f(x)=x3+3x-5  with range [1,2] f(1)=1+3-5=-4f(2)=8+6-5=9 1st Iteration: Let a=1, b=2…

Q: ) Find the integration: V1-X

A: Given integration, ∫032dx1-x2

Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: Evaluate definite integral.

A:

Q: 1. у %3D 4x2 — 3х — 2.

A:

Q: Find the average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to…

A: Since it is known that the average rate of change can be calculated using the formula…

Q: 3 dx V16-x²

A:

Q: Integrate x sqrt of (x+4) dx using algebraic substitution

A:

Q: Int(sqrt(4-x^2))

A: Substitute x=2sin(u) ⟶ u=arcsin(x/2)dx= 2cos u du

Q: Use differentials to approximate the value of (2.001)’.

A:

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

A:

Q: find integral  sqrt ( x2 - 9 )dx

A: Given: I=∫x2-9dx we know that ∫x2-a2dx=x2x2-a2-a22lnx+x2-a2+c                                ..1

Q: Find the first derivative by applying the appropriate rules. DO NOT SIMPLIFY the algebra. (a) fx)…

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Q: sinh 2x cosh 3xdx.

A:

Q: Su+1 dn th-2

A: I =   ∫135x + 1x2 + x - 2dx    = ∫135x + 1x2 + x - 2dxWriting5x + 1  = A (2x + 1) +BOn solving , A…

Q: Evaluate integral x^2e^-x^3 dx

A:

Q: Evaluate ( Sech²(In x) dx

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: The integral factor transforms the equation from not exact equation to an exact equation

A: We use the definition of Exact differential equation to obtain the answer of the given question.

Q: Solve for x: tanax=-1 -atanx

A:

Q: Find the intergral of (5-4x)/(√(12x-4x^2-8) ) dx

A: It is given that,               (5-4x)/12x-4x2-8dx     we have to integrate it.

Q: Integral of 14x2/sqrt 49-x2 dx

A:

Q: Find the third derivative of y = (8x 1) solution and upload it on the designated field in jpeg or…

A: The given equation is y=8x-114to find the third derivative of the given function. Differentiation is…

Q: calculate the integral.

A:

Q: Find the indefinite integral

A: Consider the integral: I=∫sec42x5dx……1

Q: Find the indefinite integral ∫ x2 sech2 x3 dx

A: We have to find indefinite intrgral  ∫x2sech2x3dx We have ∫x2sech2x3dx  Take x3=t⇒3x2dx=dt⇒x2dx=13dt…

Q: ㅠ -π sec xdx. 3

A:

Q: (0.2t25x+3x²) dx

A: We have to find the value of ∫050.2+25x+3x2dx using the Trapezoidal rule We take that the number of…

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,