e' – 3 dt Ve' – 3 и

Q: cosh cosh 1x dx

A: To Determine: find the integral  Given: we have ∫cosh-1xdx Explanation: we have integral ∫cosh-1xdx…

Q: 5+x*dx

A:

Q: Evaluate the integral / -2(In x)? dx

A: Given,         ∫-2lnx2dx

Q: Use integration by parts to evaluate the integral: In(s)ds

A: Given, To Evaluate

Q: Evaluate the integral or show that it is divergent.

A:

Q: Use a table of integrals to evaluate the definite integral.

A:

Q: ) 「ざs")dx

A:

Q: evaluate the given integral.

A:

Q: @ evaluate the indefinite integral fxº ex* dx

A: Given problem:- ∫ x8 ex^9 dx

Q: Find the indefinite integral: [Inx)" dx

A: Simple integration problem.....

Q: Calculate the following integral by Simpson's method 3/8 with n= and verify the error obtained. In…

A:

Q: Evaluate the integral, if it exists.    ∫0T (x4 - 8x  +7) dx

A:

Q: Consider the integral (In(x))° dx:

A:

Q: Evaluate the integral dx et – e-x

A:

Q: Evaluate the integral

A: To integrate,

Q: Evaluate the integral S dx x In x

A: Given, ∫1x ln(x)dx

Q: Use integration by parts to evaluate the definite integral. t° In(t)dt

A: Given that, I=∫1et2ln(t) dt we have to calculate the value of the integral.

Q: Evaluate the given integral. Use integration by parts 4x' In(5x)dx

A:

Q: Find the integral of dx Vx+1

A:

Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

A:

Q: Find the integral

A:

Q: Find formulas for the functions represented by the integrals.

A:

Q: Evaluate the integrals.

A: We have to evaluate ∫15dx Solution: We know that ∫dx=x Evaluating the given integral,…

Q: Evaluate the integral.

A:

Q: Evaluate the following integral using integration by parts. - 14t dt

A:

Q: Evaluate the integral. S-x cos(3x) dx

A: Use integration by parts method

Q: Evaluate the integrals

A:

Q: Evaluate the improper integral attached with this question.

A:

Q: 4. f In (2x + 1) dx =

A:

Q: dx Ух — 12

A:

Q: Evaluate the integral

A: The integral is given by,

Q: Evaluate the given integral with suitable substitution : (36z + 36) dr

A:

Q: Evaluate the definite integral using integration by parts.

A: Recall the following fact.

Q: Solve the following integral using integration by parts: In finx dx √x

A: To evaluate the given integral∫ln(x)xdx using integration by parts.

Q: Evaluate the integral. (In(x))² x3 dx

A:

Q: Find the integral of f(x³ + 1) Inx dx

A: Given :∫x3+1lnx dx

Q: or show that it is divergent Evaluate the integral dx 10

A:

Q: t3 et" dt

A: Given, ∫t3e-t4dt We have to evaluate the indefinite integral.

Q: 1. Use the table of integrals to integrate the followin a) S sin ) s in () dt

A:

Q: Evaluate the integral. x² + 25 dx of

A:

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. In 2 tanh x dx

A: ∫02tanhx dx=∫02sinhxcoshxdxUsing formula ∫f'(x)f(x)dx = ln|f(x)| +cHere , f(x)=sinhx , f'(x)= coshx

Q: In 3 | (1– x)e"dx X — х In 3

A:

Q: Evaluate the integrals in ∫dx/1 + ex

A:

Q: fx' Inx dx.

A: Given ∫x5ln(x) dx

Q: dt t/ 12 1r² – 16

A:

Q: Use integration by parts to evaluate the definite integral. 4t2 In(t)dt

A: We have to evaluate ∫1e4t2 ln(t) dt  by using integration by parts.

Q: Evaluate the integrals using integration by parts. ∫θ cos πθ dθ

A: Given: ∫θcosπθdθ

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.