Differentiating Integrals


In Exercises 75–78, find dy/dx.
________
y = ∫₂ˣ √ 2 + cos³t dt

Evaluate the integrals in Exercises 47–68.

∫₀^π/3 sec² θ dθ

Find the areas of the regions enclosed by the curves and lines in Exercises 15–26.

y = 2 sin x, y = sin 2x, 0 ≤ x ≤ π

Area

In Exercises 11–14, find the total area of the region between the graph of ƒ and the x-axis.

ƒ(x) = x² - 4x + 3, 0 ≤ x ≤ 3

Evaluating Indefinite Integrals

Evaluate the integrals in Exercises 37–46.

∫ 2(cos x)⁻¹/² sin x dx

Find dy/dx if y = ∫ₓ¹ √(1 + t²)dt.

Explain the main steps in your calculation.

If ∫²₋₂ 3ƒ(x) dx = 12, ∫⁵₋₂ ƒ(x) dx = 6, and ∫⁵₋₂ g(x) dx = 2, find the value of each of the following.

e. ∫⁵₋₂ ( ƒ(x) + g(x) ) dx

5