Evaluate the following integral. x2 dx V1- 144x x2 dx = V1-144x? (Type an exact answer. Use parentheses to clearly denote the a

Q: Evaluate the following integrals using the appropriate technique. dx (a) S (b) Sp5lnp dp 5-3x

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Q: Answer the following integral related questions. -3 I = L,(3x² – 2x + 1) dx, evaluate I;

A: We know that ∫xndx=xn+1n+1+C, where C is the integration constant. We need to use this formula to…

Q: Evaluate the following integrals i. SxIn(x+1)dx sin (Inx)cos (Inx), 2 ii.

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Q: Find the exact value of the definite integral below, using the substitution u = x - 1²/1. X (√6+√2)…

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Q: Approximate the following integrals using the Trapezoidal rule. 0.5 [h=24 dx x-4 a. [x² dx 10.5 b.

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Q: 3.) 124-1|dx Evalnate: dt given taat Ina = 9 Evalmate t

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Q: x2 + 2 dx x° + x •T/2 5. 3 6. t cos (t) dt

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Q: Evaluate the given integral. Use exact values. – 2x – 14 dx (x + 3)(x – 5) +C

A: topic - indefinite integral

Q: 7. Į V1- xdx 8. ſ e2x dx

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Q: Evaluate the following integrals dx V9 - x?

A: Given that, ∫x29 - x2 dx           ...(1) We can do this with trigonometric substitution. Consider,…

Q: . Evaluate the following integral by using the substitution x =6sin0: 1 dx x'V36 – x²

A: Consider the integral: ∫1x236-x2dx…

Q: evaluate the definite integral using the values below. 23 dx = 320, a de = 16, dx = 4 2 34. z da

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Q: Evaluate the following integrals. i) S Vs+ + e dy i) /x' Vx? - 1 dx x+2 dx x-+4x-2 iii)

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Q: Evaluate the following integral as it is written. 1 4x 3xy dy dx 0 x3 1 4x 3xy dy dx = 0 x3…

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Q: Evaluate the given definite integral using appropriate substitution: 8e2a dx @ 4e4 – 4 A © 4e4 + 4…

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Q: For what values of a is each integral improper? Explain.

A: (a) consider the integral ∫a5dxx+2.

Q: Use the value of the first integral I to evaluate the two given integrals.

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Q: Determine the following integral using the indicated substitution.

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Q: - dx 5x² +3 c)

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Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: Evaluate the following integral. Enter an exact answer. •3 4 3 dx x3

A: Topic = Integration As per guidelines , At a time only one question can be answered,

Q: 17 e- dx x=0

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Q: sin x cos? x dx

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Q: et dx 2x

A: To evaluate the given interval, ∫exe2x+5dx We use the method of substitution to evaluate the…

Q: Q4 Evaluate the following integrals cosh? (=) dx -In2 1 - fe 2 - cosh(lnx) dx

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Q: Use any appropriate method to evaluate the following integral: (x^3)*(e^(x^2)) dx

A: Simple Integration problem....

Q: Evaluate the following improper integral. Give an exact answer. 1. dx 2/3

A: Given that ∫051x23dx, we have to evaluate the following improper integral.

Q: Evaluate the following integrals i. L Ix| e(1+x*) dx -0.5 ii. So x cosh(x² + 1) dx

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Q: -dx (x+3)(x²+5)

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: To calculate the integral

Q: Evaluate the following integrals.

A: Given integral is  Let us substitute  u=ex⇒du = exdx⇒dx=e-xdu ∫dxex1-e2x=∫duu21-u2

Q: Find the following integral, given that f (x) dx = 10 and | 6)*dx = 14. 9. b.

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Q: Evaluate the following integrals using the substitution method. Answer numbers 1-2. Show your…

A: NOTE: You have posted multiple questions, we have solved the first question for you, if there is a…

Q: 2. x² V1-x? dx_

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Q: Use Simpson's rule to find the value of the following integral -3x² dx -0.9 e 0.1 where n=4

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Q: dx (6-x²)3/2 S"_ tan (x)dx

A: On solving these integration we will get

Q: Evaluate the following integral. -0.8x dx 3 e S. -0.8x dx = 3 e (Use C as the arbitrary constant.)

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Q: Evaluate the following integral as it is written. 1 2x ху dy dx 0 x? 1 2x ху dy dx %3D (Simplify…

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Q: Evaluate the following integrals: dx x In x 2.S da 1+x 1+x?

A: 1. ∫dxx ln x2. ∫1+x1+x2dx

Q: 1 36* dx V6* + 3 2x dx x2 + 2x + 5

A: The given integrals are: ∫0136x6x+3dx and ∫2xx2+2x+5dx

Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: 16. | (ez/a – e-xla)dx. n/3 sec 0 tan 0 do. Vesec e 17.

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Q: Evaluate the following integral by appropriate method: L, V2 + lx[ dx

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Q: Evaluate the following integral xe -dx J 1+2ex?

A: The given integral is I=∫xex21+2ex2dx Solving the integral using substitution.

Q: Evaluate the following integrals: xex dx 2. xe/2 dx 1.

A: Given: I1=∫xe5xdx, I2=∫xex2dx For evaluating given integral, we use integral by parts theorem…

Q: dx 3 Vx Vx (1+Vx)²

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Q: Sx² Vx – I dx

A: Given query is to find the value of integral.

Q: The value of the integral is: b 12 f(x) dx = a

A: Given that the graph of the function  To find the definite integral that represents the shaded area

Q: 3x Se 3x-e dx

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Q: Use the value of the first integral I to evaluate the two given integrals.

A: ∫01x3-2x dx=-34