Find dy/dx if y = ∫(From cos x to 0) 1/(1 - t²) dt.


Explain the main steps in your calculation.

           10           10

Suppose that Σ aₖ = -2 and Σ bₖ = 25. Find the value of

           k = 1          k = 1

  10

c. Σ (aₖ + bₖ - 1)

  k = 1

Find the area of the “triangular” region bounded on the left by x + y = 2, on the right by y = x², and above by y = 2.

Evaluate the integrals in Exercises 47–68.

_

∫₁⁴ (1 + √u)¹/² du

√u

Evaluate the integrals in Exercises 47–68.

∫⁰-π/3 sec x tan x dx

           20           20

Suppose that Σ aₖ = 0 and Σ bₖ = 7. Find the value of

           k = 1          k = 1

  20

a. Σ 3aₖ

  k = 1

Evaluate the integrals in Exercises 37–46.

∫(sin 2θ - cos 2θ)/(sin 2θ + cos 2θ)³dθ