Scaled

Mathematics Methods · Unit 3 · Topic 3.2

Integrals

5 free questions, 4 calculator-free and 1 calculator-assumed, with worked solutions written like marking keys.

Calculator-freestandard

Evaluate ∫03(3x2−4x) dx\int_0^3 (3x^2 - 4x)\,dx.

Calculator-freestandard

Evaluate ∫12(6x2−2x+1) dx\int_1^2 (6x^2 - 2x + 1)\,dx.

Calculator-assumedfoundation

Determine the area enclosed by y=x2y = x^2, the xx-axis, and the lines x=0x=0 and x=3x=3.

Calculator-freestandard

Evaluate ∫0πsin⁡x dx\int_0^{\pi} \sin x\,dx.

Calculator-freefoundation

Given ∫02f(x) dx=5\int_0^2 f(x)\,dx = 5 and ∫25f(x) dx=3\int_2^5 f(x)\,dx = 3, determine ∫05f(x) dx\int_0^5 f(x)\,dx.