Take this Quiz: A-Level Maths: Integration | Zestly

Question 1

Which of the following integrals correctly represent the area bounded by $y = x^2$ and $y = 4$?

Accepted Answer

$\int_{-2}^{2} (4 - x^2) dx$

Question 2

Evaluate $\int_{1}^{e} \ln(x) dx$ using integration by parts.

Accepted Answer

$1$

Question 3

Which substitutions are appropriate for evaluating $\int x \sqrt{x+1} dx$?

Accepted Answer

$u = x+1$

Question 4

Solve the separable differential equation $\frac{dy}{dx} = xy$ given $y(0) = 1$.

Answer

$y = e^{x^2/2}$

Answer

$y = e^{xy}$

Answer

$y = \ln(x) + 1$

Answer

$y = x^2 + 1$

Question 5

Which of the following are true regarding the definite integral $\int_{a}^{b} f(x) dx$?

Answer

$\int_{a}^{b} f(x) dx = -\int_{b}^{a} f(x) dx$

Answer

$\int_{a}^{b} f(x) dx = \int_{a+1}^{b+1} f(x) dx$

Answer

$\int_{a}^{c} f(x) dx + \int_{c}^{b} f(x) dx = \int_{a}^{b} f(x) dx$

Answer

$\int_{a}^{b} f(x) dx = f(b) - f(a)$