O Use integration by part ax Cosbx dx

Q: Evaluate the integral. x sec (3x) dx + C

A: Topic = Integration

Q: dx T² + 4 2

A: We have to find value of indefinite Integration.

Q: fx arccos x dx 2.

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Q: evaluate using Integration by Parts.

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Q: 0. Inx dx -2

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Q: Evaluate the integral. 4. (2x²+Vx) dx

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Q: -jwt dt ーの 2. 70

A: We have to solve given problem:

Q: Evaluate the integral. 3* dx V3* + 4

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Q: To evaluate fx (cos x2)e* dx, use integration by parts. What is the best choice for u and du?

A: Consider the provided integral, ∫ xcosx2ex2dx Evaluate the provided integral. Apply the substitution…

Q: Evaluate using Integration by Parts. -8x sin x dx + C

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Q: Evaluate the integral. x sec (9x) dx +C

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Q: Use integration by parts (Tabular) to evaluate: v xe-4x +]

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Q: Evaluate the inde integration, SX²J9+x' o

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Q: Evaluate the Integral ∫ 2tan3(x) sec(x) dx

A: To evaluate the integral: ∫2tan3xsecxdx We know that sec2x-tan2x=1 Given interal can be re-written…

Q: Find the integration Sx cos 2x dx

A: Here we have to use integration by parts to find the answer.

Q: . Evaluate using integration by parts 8. (5x - 3) sin(12x)dx = TC 6.

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Q: (メフき お! then Rind fcx) and ec3) メ+ %3D fC) = e %3D by using integration ?

A: f(x)=ex+1-f'(x) and f(1)=e

Q: (b) Use Integration by parts to show that ·4 In x ~dx= =-+2ln.x) +C

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Q: 3 3+ Vx dx

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Q: x° cos 2x dx

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Q: 1 dx x² Vx2 – 9 3.

A: Given ∫3∞1x2x2-9 dx We have evaluate the integral. Formul;a will use1.∫sinxdx=cosx2. sec2x-1=tan2x

Q: Sx9'de 1. Integrate:

A: Given :

Q: sin ydy 1+ sin y

A: We will use simple integration formula to solve this question.

Q: S x² e¹x dx

A: EVALUATE USING INTEGRATION BY PARTS  For the function x2e4x .

Q: Evaluate the integral sec^4(3x) dx.

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Q: Evaluate the integral: 5x sec (x) dx +C

A: Recall: ∫u.v dx = u∫v dx -∫dudx∫v dxdx   ( Product rule of integration) ∫ sec2x dx = tan(x)+C…

Q: dx ,2 /9 – x² 2

A: Solution

Q: JECT tinoM Use integration bu ax e cosbx dx

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Q: Prove by using integration by change in variable the ff. integral: dx = arcsec x +C xVx² – 1

A: Our Aim is to prove the given integral given below by using change of integration.∫dxx(x2-1)dx -(i)

Q: evaluate using Integration by Parts.

A:

Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

Q: sec? (4x)(3 – tan(4x))³dx

A: Given integral is,  ∫sec24x3-tan4x3dx. Substitute t=3-tan4x.…

Q: Evaluate the integral: dx V4 – x2 Jo

A: Given query is to find the value of the integral.

Q: 6. S ze 4z² dz

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Q: dx 5 + 4 sin a

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Q: Evaluate the integral. dx g4 Vx² + 3

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Q: Evaluate the integral: 9e3x dx е3x Vебх — 25 -

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Q: Use integration by parts to show that [x²³e³x² dx = 1 50 est (5x² −1)+c

A: ∫x3e5x2dxSubstitute u=x2→dudx=2x→dx=12xdu=12∫ue5uduIntegrate by parts:∫fg'=fg-∫f'gLet f=u and…

Q: Evaluate by Integration by parts (IBP): 4. x° cos 2x dx

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Q: find the inderinite integral it 2. dx 7-3x3

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Q: Find / tan- -dx using integration bv parts. TM

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Q: Evaluate the integral. x sec (8x) dx + C

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Q: evaluate using Integration by Parts.

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Q: Use the substitution x = 5 sec t to evaluate the integral / dx xVx2-25

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Q: 3+3x dx

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Q: dx 5. ≈ 16 x J dx – x2

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: 19. Use integration tables to find J(6x +7)*/(6x +7)² +16 dx

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Q: 36" dx o V6 + 3

A: We have to find out

Q: (a) In(4x) dx

A: Integration by parts:  ∫f(x)g′(x)dx = f(x)g(x) −∫f′(x)g(x)dx

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.