alleryUsing definite integration as the limit of a sum, $\int_1^2 (2x + 5)\,dx$ equals:
A$6$
B$8$
C$10$
D$12$
Answer & Solution
Correct answer: B. $8$
**Direct evaluation:** $[x^2 + 5x]_1^2 = (4 + 10) - (1 + 5) = 14 - 6 = 8$.
(The limit-of-sum approach in the textbook yields the same: $\lim_n h\sum(7 + 2rh) = 7(1) + (1)(1+0) = 8$.)
Keep practising Unit 6B: Definite Integration & Riemann Sums
Browse all Unit 6B: Definite Integration & Riemann Sums questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
∫ from 0 to π/2 sin x cos x dx =For ∫ dx / sqrt(a² - x²), let x = a sin θ. Result:∫ from 0 to 2 (x² - 2x) dx =Reduction formula example: ∫ sinⁿ x dx (for n ≥ 2) =∫ from 1 to e (1/x) dx =∫ x ln x dx (integration by parts: u = ln x, dv = x dx):∫ from 0 to ∞ e^(-x) dx =Area under y = x² from x = 0 to x = 2: