Q5. Use integration by part to evaluate ſešx sin (e4x )dx

Q: (x+ 1)dx 2. Jx2(x- 1)

A: Given: ∫(x+1)x2(x-1)dx Simplify by partial fraction decomposition.…

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: Solve Sx Joox Sx Jox) Sin (x) dx

A: We can solve the integral using integration by parts: Let u = Jo(x), and dv = sin(x) dx, then dudx =…

Q: | (5cotx – sin x) csc² x dx

A: Given integral is: ∫5cotx-sinxcsc2xdx Rewriting the integral:…

Q: 2. determine ∫12/5-2x dx by using substitution technique.

A: ∫125-2xdx  This is the integral given to us.we need to perform valid substitutions to evaluate the…

Q: x3=sin2 y differentiate?

A:

Q: sin (x²)dxdy y

A: We will solve this question by change of order of integration.

Q: S sec x dx Use Integration by parts to solve

A:

Q: Verify that i(t) = |e-t is a solution the the following differential equation. 1

A:

Q: Evaluate sin dx

A:

Q: S tan — х) dx

A: To integrate: ∫tan(x4-x)dx Solution: Given, ∫tan(x4-x)dx On simplifying further we get:…

Q: 3. Sx² tan (3x-1) dx

A:

Q: x?dx V1-x6

A: 1). To evaluate the integral: ∫x2 dx1-x6 Solution: Let substitute t=x3. dtdx=3x2dt3=x2  Substituting…

Q: S tan dx 3x -3x+4 dx x2-2x

A:

Q: Find the derivative of y = In (tanh x).

A:

Q: tanx X 1+x?

A: =?

Q: Evaluate * sin (x²) dxdy y

A: The integral is bounded by the curves: x=y,x=π,y=0,y=π The region is as shown below,

Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: 5- Evaluate: f Sin (2x7 - 3) dx x6

A:

Q: J (sec²4x) (tan 4x)dx

A:

Q: dx 1+cosx

A: Here we have to evaluate the given integration.

Q: 3hx 2. 3x dr

A: 2. We need to evaluate the following integral ∫e3lnx+e3xdx

Q: -22 (sinhx+coshx) dx

A:

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.