) = 31 + 3E, = 2E2 = 3, =4E, = 5| and A = 1| Find Ef(x) Ax! The sum in part (a) approximates a definite integral using rectangles. The Ef(x) Ax= D implify your answer.) Find the definite integral that is approximated by the sum in part a. dx

Q: calculate the integral in terms of the inverse hyperbolic functions.

A:

Q: b) (2 points) Find the exact value of the following integral. Show all your work. 1 5 + 2x + 3 4e" )…

A:

Q: (a) Evaluate the integral | 16х -dx by using substitution. 8x +2 (b) Evaluate the integral using by…

A:

Q: Solve the definite integral using usub

A: To integrate,

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

A: 16).17).

Q: Calculate the integral of y = 11 cos (8x) from 0 to Answer = Number Leave your answer in exact form…

A: on solving this we get the

Q: (b) 12 sec² 3x 1.² 0 6 + tan 3x dx

A:

Q: f (2x² + 4x + 5) dz (a) Find the Riemann sum for this integral using right endpoints and n= 3. R3…

A: Answer

Q: Find the indefinite integral by making the substitution x = 9sece. √ √x²-81 X dx Select one: O a.…

A:

Q: Evaluate the definite integrals a) | (15x2 + 6x - 7) dx = %3D ... ... b) (x- 3)2 dx = %3D ... ...…

A:

Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: Solve for a in the triple integral. (Enter your answers as a comma-separated list. f3-a-y2 ↑4-x-y dz…

A: ∫01∫03-a-y2∫a4-x-y2dzdxdy = 14/15 here we have to find value of a  so integrate this and after  put…

Q: b) By using appropriate substitution, solve the integral 7x dx. (1–4x)"

A:

Q: -3v3 dx V9+x?

A: Evaluate the intregal

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: Evaluate the Integral dx |. 1 + 2 ax X² 2

A: Consider the integration."Note that as per the rules, we are supposed to answer the first question…

Q: Find an expression in a and b for the value of the definite integral: ∫ba [2x2 + √x + 5]dx

A: Evaluating the definite integral

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.