Evaluate the integrals in Exercises 47–68.
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∫₁⁴ (1 + √u)¹/² du
√u

           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.

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 47–68.

∫₀^π/4 sec²x / (1 + 7 tan x)²/³ dx