10 dt Use trigonometric substitution to evaluate t2 Vt2 – 25 O V3/50- O v3/72. O In(7+4v3). This integral does not converge.

Q: The integral 4x dx Vx2 – 4 1 is an improper integral of typel is an improper integral of type II…

A: The given problem is solved below in detail.

Q: (b) Prove that the improper integral Ï Ï -8 -∞ converges. dx dy (1 + x² + y2)3/2

A: Consider the given improper integral, I=∫-∞∞∫-∞∞dxdy1+x2+y232 Change into circular coordinates by…

Q: Given √ 1 pdx.c A (-∞,1] B (1,00⁰) Ⓒ (-∞0,00) D (0,1) dx, determine all value/values of P for which…

A: This can be solved as follows:

Q: 25. Determine whether the improper integral J. dx diverges or converges. 1-x Evaluate the integral…

A:

Q: Find the values of p for which the integral converges. (Enter your answer as ar '1 1 9. хр (-∞<p<1)U

A: evaluate the integral and find what values of p the answer does not exist

Q: The improper integral 2 dx (x-1)* X - a) Converges to -2 b) Converges to -5 c) Converges to 0 d)…

A: solve the following

Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

Q: 1. dx .00 1 1 x 1 2. 1 (3x+1)2 8

A:

Q: 10 Detemine whether the improper miegral lo F+16) dx diverges or converges. Evaluate the integral if…

A: Given the improper integral  I=∫0∞10x(x+16)dx

Q: The integral 2 X dx 2 - Vx² – 4 3 1 is an improper integral of type I (3)% is an improper integral…

A:

Q: (1+2x) e¯* dx O Converges O Diverges

A: In the question we have to determine if series converges or diverges.

Q: 7. Determine the following integral. Also indicate if the integral converge or diverge. Show the…

A:

Q: determine whether the given integral converges or diverges. 20.∫∞0te−t dt∫0∞te−t dt

A:

Q: Given a > 0, the improper integralJa ran-ix(1+x³)' dx is convergent to In- In if: a = 1 a = 2 O the…

A:

Q: Determine whether the improper integral converges or diverges. In bxl -dx A Converges B Diverges

A:

Q: 1. Determine if the integral converges or diverges: re2" dx.

A:

Q: An improper integral J converges if : e-x dx Ocr0

A:

Q: Determine whether the improper integral diverges or converges. dx 1.co (2x-1)* 00 dx 2. x +1

A: To check weather the given Integral is converges or diverges.

Q: 11:33 dx The improper integral xVIn x converges to 2 the above diverges to -∞ the above

A:

Q: Q3) Approximate the integral e* cos x dx using the composite Trapezoidal rule with M=5 subintervals.

A:

Q: The improper integral 2e*dx is: (a)converge to 2 (b) converge to – 2 (c) convergeto 0 (d) diverge a…

A: Solution is given below:

Q: 10. Determine whether the improper integral converges or diverges 3 dx (x – 1)3 -

A: Given query is to integral converges or diverges.

Q: The improper integral dx 2 x2+4x+8 converges to 4 O None converges to 37 converges to O diverges

A: Topic- integration

Q: (b) Check the convergence of the improper integral dx. I+2

A: Improper integral

Q: The improper integral 2e*dx is: (a)converge to 2 (b) converge to – 2 (c) converge to 0 (d) diverge

A: To solve the given improper integral.

Q: 4) Determine whether the improper integral diverges a) fx'e *dx or converges: 1 b) J (7x +1)³ 1

A:

Q: 3. Show that for p> 1 and r E (0, 1), the integral below converge: dt tp

A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

Q: Determine whether the improper integral converges and, if so, evaluate it.

A: ∫56dxx-532 On integrating, we get ∫56dxx-532=∫56x-5-32…

Q: 4. Based on the definition, the integral Sx'dx. Choose an option below and explain why. -0o a. Is…

A:

Q: 4. S dy y³-2y²

A:

Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: Consider the following improper integral: eV2r dx 00 It can be guaranteed that the integral a)…

A:

Q: 2 36. 0. dx, T20

A:

Q: 00 The improper integral | 2e 2e*dx is: -00 (a)converge to 2 (b) converge to – 2 (c) converge to 0…

A:

Q: T/2 2+ sin x dx (iii)

A: The integral converges  see below the calculation and steps

Q: 2. Determine the convergence of the improper integral e² In x dx.

A: Take the integral, ∫0∞xlnx=lnxx22-∫0∞1x.x22dx=x2lnx2-x240∞=∞ As after taking x→∞ the limit of the…

Q: The improper integral 1 dx converges to '5 Vx-5

A:

Q: (b) Prove that the improper integral ]] converges. dr dy (1 + x² + y²)³/2

A: Given problem:-

Q: Compute the value of the following improper integral, if it converges. (If it diverges, enter oo if…

A:

Q: Determine whether the improper integral or is divergent. S 1 1 1+2* + e²x 2x dx is convergent

A: Given the improper integral as ∫1∞11+2x+e2xdx To determine whether the given series is convergent or…

Q: 5) Prove whether or not the following integrals converge or diverge. a) Si b) S, 1 dt In(t)-1

A:

Q: Find any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

A:

Q: (a) Explain why | dr is divergent. (b) Find all value(s) of t > 0 for which the integral / 1 dx is…

A:

Q: (1+2x) e¯ª dx O Converges O Diverges

A: We have to check

Q: $²² Α) (1,∞0) B (-∞,1] (-∞0,00) Given D {0,1} dx, determine all value/values of P for which the…

A:

Q: 2. Evaluate the following improper integrals if convergent, otherwise justify why the integral…

A: We have to evaluate the following improper integrals if convergent, or justify why the integral…

Q: 1. Let p be constant, and consider the improper integral 1 d.x x (In(x))" /2 For what values of p…

A:

Q: 7. Determine whether the given integral is convergent or 1 dx? x*+1 divergent Page of a. convergent…

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.