10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =| +C

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

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Q: 6. The improper integral dx converges to /x- 5 '5 Vr-5

A: The given integral is an improper integral of second kind.

Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² –…

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Q: 6. Evaluate the integral ex e* +e-xdx

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Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: Evaluate the double integral : (3 – 8z) dz dy

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Q: 3 Calculate the integral: dx x² V25 + x2

A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: What is the integral of x2(2-x)^(1/3) dx on the interval [1,2]?

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Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x) dx.

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Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: 3. Evaluate the indefinite integral 1 -dx x' + 3x? 3

A: Given,

Q: 8. Evaluate x dx from the definition of RS-integral.

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Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

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Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

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Q: Evaluate the double integral 1 2x+1 LL.** Select one: | None of them 113 x² dy dx

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Q: 4х+2 Evaluate the integral -dx. (Hint: Use Algebra to help further rewrite your (x² +1)(x=1)…

A: First break by using partial fraction then integrate

Q: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: =dx V2x* +3 4

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Q: 3 Estimate the integral 1 dx by Simpson's rule using n= 8. Vx3 + 5

A: Given that a integration and ask estimate value use Simpson rule when n= 8. In Simpson rule we can…

Q: Find the indefinite integral using the Chain Rule/U-substitution. 6x dx x2+5 3. 4. S 7xv3x² + 8 dx

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Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

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Q: 2. Find the indefinite integral: S (Vã+ - x + - 1) dx 6 .3 X X

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Q: 7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1…

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Q: 7 149-x2 V49-x2 Evaluate the integral| dz dy dx. 7 49-x J49-x S S S dz dy dx = 0 0 (Type a…

A: ∫07∫049-x2∫049-x2dzdydx

Q: 3 9-x 9-x2 Evaluate the integral dz dy dx. 0 0 . 0

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Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

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Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: Step by step

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Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: Show that integral 0 to infinity  x2 e -x2  dx = 1/2 integral 0 to infinity e -x2  dx

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Q: Match the integral expression on the left to an equal expression on the right. Ssin(3x)sin(4x)dx -…

A: Let's find.

Q: 2. Use integration by parts to establish the reduction formula: Sx" cos x dx = x" sin x – n x"-1 sin…

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Q: 2. Evaluate the integral x(3 – 5x) (3x – 1)(x – 1)2 dx

A: To solve the following integral

Q: 6. Evaluate the integral. x³e2x dx

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Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: csch (2sin 2x)dx 1. V1-4x

A: Given problem:-

Q: 6. Evaluate the integral dx (4x2 + 1)(x² + 4)

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Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: -3 evaluate the integral (x2 – x + 2) dx using its definition.

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Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: 10. Find the indefinite integral. x – 2 dx x² + 1 -

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Q: Compute the indefinite integral 2. - 4e²² + 6z – 5) 5) dx.

A: We know that integration of ex is ex . And integration of 1/x is lnx. Integration of xn is xn+1/…

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: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

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