Evaluate the integrals in Exercises 37–46.


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

           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.

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

Explain the main steps in your calculation.