x2 Evaluate : p.v J_∞ (x2+3)² dx

Q: = - 1) ex²-x dx x. Use the substitution method to rewrite the function in the integrand, (18x – 1)…

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Q: Evaluate the integral. V3/2 5x2 dx V1 - x2

A: Consider the trigonometric identities 1)  cos2x = cos2x - sin2x = 1- 2sin2x 2)  cos2x + sin2x = 1 3)…

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

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Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: Evaluate the integral. V3/2 19x2 dx V1 - x2

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Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: dx 7. S x V9x2-1

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Q: Evaluate the integral. dx 4 a > 0 (a² + x²)3/2?

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Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

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Q: 5. Evaluate f* cos xdx ´using integration by parts.

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Q: 78x Sinx d Show that it is Conv drichlet t. divergent by

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Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: Evaluate the integral. 9 17 1+ x2 dx V1- x2 +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: 3 Evaluate the integral: dx 2 Vx -1

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Q: Evaluate the definite integral. "1/3 3 dx V1- 9x²

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Q: 4x2 Calculate the integral: dx 3/2

A: I use trigonometric substitution to calculate this integral to see full solution please visit 2nd…

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

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Q: -dx. Q5. Evaluate the integral / Tx² + 1)(X · x – 2)

A: Given  α=5 ,β=8 ,γ=13,λ=2 ,θ=5 , η=3 ,ω=2 . To rewrite the given integration by using α=5 and λ=2 .…

Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: Evaluate 2Sin x´dx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A: i)Given:        ∫242sinx2dx   Mid-point rule:       ∫abf(x)dx=∆xfx0+x12+fx1+x22+fx2+x32+...…

Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 4 x2 Calculate the integral: dx V64 – x2

A: Consider the integral ∫4x264-x2dx Here, the objective is to find the indefinite integral using…

Q: Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

A: I have use the substitution

Q: (2– sec²x) ln (# /e)scc³x sec(3A – x) What should be the value of A for to be integrable using the…

A: Let's find.

Q: dx Use Simpson's method to evaluate o x² + 9 Hence estimate error.

A: In this question first, we have to evaluate the integral through normal integration and find the…

Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

Q: prove that (d/(dx))(sec^-1x)=1/(xsqrt(x^2-1))

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given that, fx=x2+4x4-4x2+16 Differentiation formulae: ddxuv=uddxv+vddxu    [Product rule]…

Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: Q18: Evaluate the definite integral: 4x dx V1 + 2x²

A: To find the definite Integral  Substitute 1+2x^2 = t and change the limit accordingly

Q: Evaluate the integral Зx2 — 4х — 9 A В + C dx using x3 – 2x2 – 9x + 18 - 2 x +3 – 3* х — х — 3x2 –…

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Q: dx Use Simpson's method to evaluate o x² +9 Hence estimate error.

A: To evaluate ∫02dxx2+9, let n=4. The Simpson's rule says that…

Q: Evaluate the integral 1 2 (5e Vx - sec 2) dx. ух е XM

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Q: Evaluate the integral. dx i. 2 x²Vx2–1°

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Q: Q/Evaluate Integral:- sec2 3x dx tan23x-3 tan3x+2

A: To evaluate the integral:

Q: 4. Prove 1 < | V1+ a dx <2 0,

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Q: Q2 ) Use the Simpson's rule with (n = 4) to estimate thef²n sinx dx . 2

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Q: V312-x2 31 dydx = %3D 1+x2+y2 Jo int062) ○ 푸n(31) 2 O In(962) O TIn(962) O 2nln(31)

A: Given: I=∫031∫0312-x221+x2+y2dxydx   Now convert to polar coordinate to solve the given integral. As…

Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

Q: Evaluate the integral. 9. dx J2 (x² – 1)3/2

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Q: 4x2-3 f (x) 2х3+x2+7

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate:

Q: the integral (dx)/(xsqrt4x2+1)

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