2 Evaluate the improper integral e2a dx, if exists.

Q: Estimate the error if e-² is approximated by 1-2² +21 in the integral L²e-2². dx.

A:

Q: 4. Evaluate the improper integral dx +e"

A: We know that, ddxex=ex ∫1a2+x2dx=1atan-1xa+c tan-1(1)=π4 tan-1(∞)=π2

Q: Evaluate the integrals

A: Integration means addition. It is used for adding continuous function which can't be added by simple…

Q: Evaluate the integral | 3 dx. V9x -4

A:

Q: Show for Re(z) > 1 dx = r(2) ((2). et - 1

A:

Q: A) Evaluate the following integral (x - 1)(x − 2)(x-3) -

A: Given, ∫1x-1x-2x-3dx

Q: 14. Evaluate the integral 2 Jo dx 2x + 3x + 1

A: ∫0122x2+3x+1dx Factor the denominator  ∫012 (2x+1)(x+1)dx Now apply partial fractions   2…

Q: Show for Re(z) > 1 -dx r(2) ((2). 1 er 0.

A:

Q: compute the derivate

A:

Q: Evaluate each integral. #1) [(x' +2x)dx 5dv #2) | v(In(v)) #3) [(x*e*)dx

A:

Q: Evaluate the integral. r1/3 -1 2x = xp J1/7

A: ∫1713-12xdx=∫1713-12.1xdxWe know that ∫1x dx=ln(x)+cSo, ∫1713-12xdx=∫1713-12.1xdx

Q: Q3:Evaluate the integrals T|(x+y+1)dxdy -1-1

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: . Show for Re(2) > 1 -dr r(2) ((2). e - 1

A: The given problem is to show the following integral is the product of zeta function and gamma…

Q: Show for Re(z) > 1 ex – 1 dr = T(z)5(2). et – 1

A:

Q: The sum can be written as a single integral in the form Determine a and b. a = b = 5 ·[³1(x) dx - 16…

A:

Q: Show for Re(2) > 1 ez - 1dr = r'(z) 5(2). %3D 0,

A:

Q: Show for Re(z) > 1 -dx = r(z) (2). et - 1

A: