Questions from General Calculus

Q: Evaluate the following definite integrals. ∫1 e ln x

Evaluate the following definite integrals. ∫1 e ln x dx

Q: Evaluate the following definite integrals. ∫0 π esin x

Evaluate the following definite integrals. ∫0 π esin x cos x dx

Q: Evaluate the following definite integrals. ∫0 π/4

Evaluate the following definite integrals. ∫0 π/4 tan x dx

Q: Determine the integrals by making appropriate substitutions. ∫ xex2 dx

Determine the integrals by making appropriate substitutions. ∫ xex2 dx

Q: Evaluate the following definite integrals. ∫0 1 x sin

Evaluate the following definite integrals. ∫0 1 x sin πx dx

Q: Evaluate the following definite integrals. ∫0 π/2

Evaluate the following definite integrals. ∫0 π/2 sin(2x – π/2) dx

Q: Use substitutions and the fact that a circle of radius r has

Use substitutions and the fact that a circle of radius r has area πr2 to evaluate the following integrals. ∫-π/2 π/2 √(1 - sin2 x) cos x dx

Q: Use substitutions and the fact that a circle of radius r has

Use substitutions and the fact that a circle of radius r has area πr2 to evaluate the following integrals. ∫0 √2 √ (4 - x4) * 2x dx

Q: Use substitutions and the fact that a circle of radius r has

Use substitutions and the fact that a circle of radius r has area πr2 to evaluate the following integrals. ∫-6 0√ (-x2 - 6x) dx

Q: Find the area of the shaded regions. /

Find the area of the shaded regions.