Homework

Problem 1 · easy

Find ∫ x^4 dx.

Problem 2 · easy

Find ∫ x^6 dx.

Problem 3 · easy

Find ∫ 3 dx.

Problem 4 · easy

Find ∫ 5x^2 dx.

Problem 5 · easy

Find ∫ (x^2 + 3x) dx.

Problem 6 · easy

Find ∫ (4x^3 - 2x + 1) dx.

Problem 7 · medium

Find ∫ x^(-3) dx.

Problem 8 · medium

Find ∫ x^(1/2) dx.

Problem 9 · easy

Find ∫ cos(x) dx.

Problem 10 · easy

Find ∫ sin(x) dx.

Problem 11 · easy

Find ∫ sec^2(x) dx.

Problem 12 · medium

Find ∫ (x + 1/x^2) dx. Assume x > 0.

Problem 13 · medium

Find ∫ (2x^3 - x^2 + x - 1) dx.

Problem 14 · easy

Find ∫ 7x^6 dx.

Problem 15 · medium

Find f(x) given f'(x) = 3x^2 and f(0) = 5.

Problem 16 · medium

Find f(x) given f'(x) = 2x - 1 and f(1) = 0.

Problem 17 · medium

Find f(x) given f'(x) = cos(x) and f(0) = 2.

Problem 18 · medium

A ball has a(t) = -10 m/s^2 and v(0) = 15 m/s. Find v(t).

Problem 19 · medium

Using v(t) = -10t + 15 from Problem 18 and s(0) = 0, find s(t).

Problem 20 · medium

When does the ball from Problem 18 reach its highest point?

Problem 21 · medium

Find ∫ (sqrt(x) + 1/sqrt(x)) dx.

Problem 22 · easy

Find ∫ 12x^11 dx.

Problem 23 · medium

Find f(x) given f'(x) = 6x^2 - 4x and f(2) = 3.

Problem 24 · medium

Find ∫ (x^2 - 1)(x + 1) dx by expanding first.

Problem 25 · medium

Find ∫ (3x - 2)^2 dx by expanding first.