Questions from General Calculus

Q: Determine the integrals by making appropriate substitutions. ∫ 2/

Determine the integrals by making appropriate substitutions. ∫ 2/ x (ln x)4 dx

Q: Evaluate the following definite integrals: ∫1/2 1

Evaluate the following definite integrals: ∫1/2 1 ln(2x + 3) / (2x + 3) dx

Q: Evaluate the following definite integrals: ∫1 2 x e

Evaluate the following definite integrals: ∫1 2 x e-2x dx

Q: Evaluate the following definite integrals: ∫1 2x-3

Evaluate the following definite integrals: ∫1 2x-3/2 ln x dx

Q: Approximate the following definite integrals by the midpoint rule, the trapezoidal

Approximate the following definite integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. ∫1 9 1/√x dx; n = 4

Q: Approximate the following definite integrals by the midpoint rule, the trapezoidal

Approximate the following definite integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. ∫0 10 e√x dx; n = 5

Q: Approximate the following definite integrals by the midpoint rule, the trapezoidal

Approximate the following definite integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. ∫1 4 ex / (x + 1) dx; n = 5

Q: Approximate the following definite integrals by the midpoint rule, the trapezoidal

Approximate the following definite integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. ∫-1 1 1/(1 + x2) dx; n = 5

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

Evaluate the following improper integrals whenever they are convergent. ∫0 ∞ e6-3x dx.

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

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