(a) Evaluate the integral 9x"e¬X dx for n = 0, 1, 2, and 3. n = 0 9. o((-") - (-1)) n = 1 е | n = 2 n = 3

Q: 1 e-r/2 dx = 1. (2m

A: Using double integral of Cartesian form and polar form.

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: 3. Evaluate the indefinite integral e* –3 -dx (e²x +1)(e* – 2)

A: Consider the equation

Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b

Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: Evaluating the integral | (2.x* +e* –-)dx gives: O A. 2 +e* – 2 In |x| +c - O. 4.x² +e* – 2 ln|x|+c…

A:

Q: x³ + 6x² + x +2 fx-1 ax + In{(x + 1)*(x² – x + 1)| +- 2 Tan Ve The resulting integral of -1 + C,…

A:

Q: 1. Evaluate the following integral: (1-e-²x) dx (a) analytically;

A: Note:- For this problem all the sub-parts  are different as methods are different. So, we can solve…

Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

A:

Q: Find the indefinite integral.

A: Let ex+e-x=v. Differentiate both sides: (ex-e-x)dx=dv Substitute v and dv in the integral…

Q: 4. dx J x Inx VInx2 -1 A C - sec-1 (In xx) + C sec-1 - In x sec-1 (In x) + C + C In x. sec-1 O A В E…

A:

Q: The value of the improper integral 42 x² e¯¤* dx 1 - 14e 14e-1 - O 14e-1 O 42e-1 O – 42e-1

A: Explanation of the solution is given below...

Q: The result of the integral 4 / (x - 1)(x + 1) is equal to -dx Select one: O none of these. ○ In…

A:

Q: Evaluate the integral. | (e7* +3e -x) dx 7X +3 e -X) dx=

A:

Q: 1. Evaluate the integrals x³e- dx

A:

Q: 1. Evaluate the ff. integral f, (5x6 + 3x³ + 6)dx ·1

A:

Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: - Evaluate the integral dx using Simpson's th rule e* – 1 3 -

A:

Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

Q: Evaluating the integral | (2x +e -)dx gives: 4 +e* – 2 ln x +c O A. 4x² +e* – 2 In|x|+c O B. x* +e*…

A:

Q: 15+0. The improper integral e* dx is

A:

Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: 24. ( (x² + 1)e*dx

A:

Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: The improper integral e-3x dx 0. equals Refer: improper integral O 1 O 1/3

A:

Q: 18x? Evaluate the integral: -dx V49 – x2 -

A:

Q: 11. The integral of an(In|4x=12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. С. 4 D. I

A:

Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

A:

Q: 5. Evaluate the integral. 1 -dx æ² – 1 a) b) S. +4 -dx x² + 4

A:

Q: 5x dx. - 6 Compute the integral x2

A:

Q: Evaluate the integral. dx (х — 13)(х — 23) (Use symbolic notation and fractions where needed. Use C…

A: Explained below

Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

A:

Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: What is the integral of x" cos ax dx ? хN sin ax А. -=S nx"-1 sin ax dx + а а хN sin ax B. n -"Sxn-1…

A:

Q: iii. Find the particular integral (P.I) of y" + 9y = cos 3x

A: To find the particular integral P.I of  y''+9y=cos 3x

Q: Can i get help step by step?

A: We separate the integral into two parts

Q: 11. The integral of tan(In|4x²|) dx is bln|sec(ln(2x)ª)|. What is b? А. 2 В. 1 D. ! С.4 4

A:

Q: a) [ ]: Evaluate the integral (4x + 1) In x dx c) [ ]: Evaluate the integral 2 dx (x – 1)(x + 4) |

A:

Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: 11. The integral of an(In|4x-12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. 2 С. 4 D.

A:

Q: Compute the integral 4x /5 – e2¤ dx. e

A:

Q: how do I find the integral of e^-xsec^2(e^-x)dx

A:

Q: Consider the indefinite integral Ва3 + 21? + 5а + 0 dx x² – 1 | Then the integrand decomposes into…

A:

Q: 12. Find the integral. (a) / e*VI+e=dx -64 1+ (b) /" 1 -dr x In a (c)

A:

Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows

Q: Find the integral. 5x* dx (5+x*)* 1 O A. 3(5+x)3 OA. 1 О в. В. +C 5(5+x*)5 Oc. (5+x)°. +C

A:

Q: The value of the integral T/2 sin x dx cos(x)e- sin Jo is: Оа. 1-е-1 O a. O b. e- sin 1 O C. С. cos…

A:

Q: 2. Integral A e3A dA

A:

Q: 23. (a) (2n )! [P,(x)]² dx 2 (n!)ª J_, (1 – x*y" dx (b) By making an appropriate change of variable,…

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.