x² to compute the integral x· V1 – x4 dx. [Hint: the Use the substitution u = FTC is great, but not every problem is best solved using it. Remember that you can chỉnk geometrically!]

Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: a) If | f (x) de f(x) dx = 2, find 1 (3f(a) – 1) de. = 7 and || - /4 (b) Estimate the value of the…

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

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Q: 1. Approximately compute the value of the following integral, as accurately as possible, using the…

A: Note:- Here, you mention function f(x) is creating little bit confusion for me. Is…

Q: The particular Integral for (D2 + 42)y = sin4x is. Yp

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Q: b) 1+x dx Approximate the integral both directly and by trapezoidal method for intervals 2 and 4.

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Q: Q2) - Evaluate the integrals: V16-x 2. 3. SA dx 4. S Vx2 +1 dx dx

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Q: Q3. Evaluate the following two integrals using both the simple trapezoidal method and once using…

A: We will use the knowledge of the simple trapezoidal method and Simpson's method.

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: -1.30 Find the value of the integral 100 √x dx by using simpson method (n = 6)?

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Q: express L−1[F(s)G(s)] in terms of a convolution integral.

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Q: Find the indefinite integral. 3 8 dt = t3 t2 +C

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Q: Q2/ Find the value of the following integrals: 1- |((x+ y)dx +(y-x)dy), when c is given by, x = cos…

A: We have to evaluate the integral is ∫cx+ydx+y−xdy. where c is given by x=cosθ, y=sinθ and 0≤θ≤2π.…

Q: express L−1[F(s)G(s)]in terms of a convolution integral.

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Q: Given dy – sin(x))dx + cos(x)dy, where C is the triangle with vertices (0, 0), (1/2, 0), and (t/2,…

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Q: Q1 - Find the reduction formula for each of the following integrals iv. In = S sinh"x dx

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Q: S(e-3y V6 + e- 3y 2y3+y -)dy y4+y2+1 -

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Q: 2 4 Q3) Evaluate the integral || xe" dy dx 0 x?

A: LetI=∫02∫x24xey2dydxchange the orderI=∫04∫0yxey2dxdyLet∫0yxey2dx=x∫0yey2dx∫0yxey2dx=ey2[x22]0y…

Q: Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it…

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Q: 3 I [(e* +x² + A\dx Дх 3 0,25 1

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Q: So S(x + 3) dy dx 3. Evaluate the double integral:

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Q: Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

A: Given function is f(x)=14πx4cos14πx, we have to integrate above function from 0 to 2. Formula for…

Q: Q2/Find the value of the integral dx 1+x² by using simpson method (n = 6)? 3

A: Find out the value of the integral using the simpson 1/3 method.

Q: 5. Evaluate the integral A by Simpsons rule with 2m = 8, and compare your result with the exact…

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Q: Q1: Verify that the given functions are solutions of the corresponding integral equations by using…

A: Given: ₵(x)=xex and ₵(x)=exsinx+2∫0xcos(x-t)₵(t) dt

Q: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

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Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: 1. Evaluate the integral r4-x² 8x cos Y dy dx Y – 4 by reversing the order of integration.

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

A: Explained below

Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

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: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: -2 Evaluate the definite integral S: 1 dx. 1 x+a²

A: general answer is Ln|(2+a^2)÷(1+a^2)| Where a = -3/5 Final answer is Ln|59/34|

Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: n/4 3x Approximate the integral e "sin(2x)dx using both Simpson's rules with n = п/12

A: Given: I=∫0π4e3xsin2xdxn=π12

Q: Q.1) Evaluate the following integral ez dx (2e2 – 4e* – 1) - -

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Q: By the even extension method applied to the function f(x)= e-16z, where a > 0, the value of the…

A: The given function is, f(x)=e-16x,x>0

Q: (a) Use integration by parts to evaluate T/4 | 0 sin(20) dð . (b) Use the substitution u = 1+ x to…

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Q: 1. Evaluate the integral Vi-x² ex?+y*dydx.

A: 1. The given integral is, ∫01∫01-x2ex2+y2dydx. Convert the integral into polar coordinates as…

Q: Evaluate the definite integral. *2 e 1/x* dx J1 +s

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Q: dy y(y²+1)

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Q: Evaluate the integrals dx Så (4-x²)²

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Q: Find the value of the constant C for which the integral 5x 5C dx 2 X² + 1 Зх + 1 converges. C = 3…

A: Convergence of integral

Q: Q1\ Evaluate the integrals: 10 A. S- V16+x2 В. Г(3 — 2х)-5 dx

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Q: 2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

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Q: Q2/ Find the value of the following integrals: 1- [(* |(x+ y)dx + (y - x)dy), when c is given by, x…

A: The line integral ∫CF1dx+F2dy involves the integration over a specific path. In this problem, we…

Q: = "+1 + C. 2. The power rule for integrals is x" dx a. Evaluate f da = fx2dx. n+1* 1 b. What goes…

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