Homework

Problem 1 · easy

Evaluate ∫[0 to 2] x dx.

Problem 2 · easy

Evaluate ∫[1 to 3] x^2 dx.

Problem 3 · easy

Evaluate ∫[0 to 1] (2x + 1) dx.

Problem 4 · easy

Evaluate ∫[0 to pi/2] cos(x) dx.

Problem 5 · easy

Evaluate ∫[0 to pi] sin(x) dx.

Problem 6 · medium

Evaluate ∫[1 to 4] sqrt(x) dx.

Problem 7 · medium

Evaluate ∫[-1 to 1] x^3 dx.

Problem 8 · medium

Evaluate ∫[0 to 2] (x^3 - x) dx.

Problem 9 · easy

Evaluate ∫[0 to 1] x^4 dx.

Problem 10 · easy

Evaluate ∫[0 to 3] 5 dx.

Problem 11 · medium

Evaluate ∫[1 to 2] (3x^2 + 2x) dx.

Problem 12 · easy

Find d/dx [∫[0 to x] t^5 dt].

Problem 13 · easy

Find d/dx [∫[0 to x] sin(t^2) dt].

Problem 14 · medium

Find d/dx [∫[1 to x^2] t^3 dt].

Problem 15 · medium

If v(t) = 2t - 4 on [0, 4], find the net displacement.

Problem 16 · medium

Find the total distance traveled for v(t) = 2t-4 on [0,4].

Problem 17 · easy

Evaluate ∫[0 to 2] x^3 dx.

Problem 18 · medium

Evaluate ∫[-2 to 2] (x^2 + 1) dx.

Problem 19 · medium

Find the area between y = x^2 and y = x on [0, 1].

Problem 20 · medium

Find the area between y = x and y = x^3 on [0, 1].

Problem 21 · easy

Evaluate ∫[0 to pi/2] 2cos(x) dx.

Problem 22 · medium

A spring (k=100 N/m) is compressed 0.2 m. Find the work done.

Problem 23 · easy

Evaluate ∫[0 to 1] (1 - x^2) dx.

Problem 24 · challenge

Evaluate ∫[1 to e] (1/x) dx. (Answer in terms of e or ln.)

Problem 25 · challenge

Evaluate ∫[0 to 4] |x - 2| dx.