-- Solve the following integral with details 1 13e"/4cos² 0 ,² dr sined60 o do = x 32παο X= ? ifforontial oguntion (25p (h and a are variables)

Q: 16. Use substitution to find and evaluate the definite integral. Give your answer in exact form. T/3…

A:

Q: Find each of the following integrals in at least 3 or 4 steps, as indicated. S sin*2xcos 2xdx 1.

A: ∫sin4(2x) cos3(2x) dxWe substitute  u=2x⇒ 2dx= du ⇒ dx= 12du :=∫sin4(u) cos3(u) 12du=12∫sin4(u)…

Q: 17) Calculate the indefinite integral S-5dx √4-16x² 16) Evaluate the definite integral Š - 0 3…

A: 16).17).

Q: * = (5, 4, 3, 2, 1) %3D What is r2?

A: x2 is second element from left.

Q: 12 cos6x. sin³ xdxCalculate "/2 3 the integral

A: It is integral problem.

Q: 3.(Total: s) Evaluate the following integrals 3a. (1-s) x arctan(3r) dx = %3D 3b.( s) sin(5z) c dr =…

A: Explanation of the answer is as follows

Q: 13) Calculate definite integral. Give answer as a fraction in lowest terms (x2 – 2x-3 + 3)dx

A: We will use integration rules

Q: Find the indefinite integral. х cos 9пх2 dx

A:

Q: 1. 4x° sec .3 x dx cos Va dx Væ csc Va x2 -dr 2.

A:

Q: I. Solve the following integrals: 1. (x²Inx+ sin ¹2x + sec³x)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.