The definite integral and the Newton–Leibniz formula
Answers are for parents and teachers.
1
Compute ∫₀² (3x² − 2x + 1) dx.
6
2
Find the area of the figure bounded by the graph of y = 4x − x³ (0 ≤ x ≤ 2) and the Ox axis.
4
3
Compute ∫₀^(π/4) cos 2x dx.
(1/2) sin 2x|₀^(π/4) = 1/2.
4
Compute ∫₁⁹ (1/√x) dx.
4
5
If ∫₀³ f dx = 5 and ∫₃⁷ f dx = −2, find ∫₀⁷ f dx and ∫₇³ f dx.
By additivity: 5 + (−2) = 3. ∫₇³ f dx = −∫₃⁷ f dx = 2.