Questions from General Calculus

Q: Evaluate the following improper integrals whenever they are convergent. ∫-∞

Evaluate the following improper integrals whenever they are convergent. ∫-∞ 0 e4x dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫-∞

Evaluate the following improper integrals whenever they are convergent. ∫-∞ 0 8/(x - 5)2 dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫-∞

Evaluate the following improper integrals whenever they are convergent. ∫-∞ 0 6/(1 - 3x)2 dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫-∞

Evaluate the following improper integrals whenever they are convergent. ∫-∞ 0 1/(24 – x) dx

Q: Determine the integrals by making appropriate substitutions. ∫ x2/(

Determine the integrals by making appropriate substitutions. ∫ x2/(3 - x3) dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫

Evaluate the following improper integrals whenever they are convergent. ∫0 ∞ e-x / (e-x + 2)2 dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫-∞

Evaluate the following improper integrals whenever they are convergent. ∫-∞ ∞ e-x/(e-x + 2)2 dx

Q: If k > 0, show that ∫0 ∞ k

If k > 0, show that ∫0 ∞ k e-kx dx = 1.

Q: If k > 0, show that ∫1 ∞ k

If k > 0, show that ∫1 ∞ k / xk+1 dx = 1.

Q: If k > 0, show that ∫e ∞ k

If k > 0, show that ∫e ∞ k / x(ln x)k+1 dx = 1.