Q2. Use integration by parts to evaluate the following Integral 2 COs x² dx

Q: Find d2y/dx2 for the following functions: b) y = cos*(sec? 3x) 4 = COS

A: We are given : y=cos4(sec23x) ⇒dydx=4cos3(sec23x).(-sinsec23x).2sec(3x)sec 3x.tan…

Q: Integrate the following expressions: Sex-e (2x – e*). dx !! (x + cos2x). dx "/2 X cos2x.dx

A:

Q: Integrate by parts the following: Se²x e2x sin(3x) dx

A: We have to find value of given integration. Let value of integration is I and sin(3x)=first…

Q: Integrate the following. 3. f sec?x dx tanx

A:

Q: sinx I. dx by using suitable substitution. cosx+5cosx+6 Sx5ex* dx I. S sin²xcos*xdx I.

A:

Q: Evaluate the following definite integral : 8. 1 + X dx X

A: Given,          ∫08x1+xdx

Q: dx dy dz

A:

Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: 3. Find each definite integral: A. S(x- 3x) dx | -1 B. ( 2cosx + 2sinx dx

A:

Q: : A) Solve the following integral: S x5J4(x) dx.

A: It is known that ∫xvJv-1x dx=xvJvx.

Q: 2 1². Evaluate I e4-22² dx needed, round part b to 4 decimal

A:

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

A:

Q: Evaluate: Jx?cos(2x)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.