Integral Calculus and Differential Equations

Learn integration patterns, definite integrals and first-order DE setup.

Level

Exam-focused

Study Time

24 min

Exam Relevance

High (method selection and algebraic patience)

Core concepts

5 quick questions from the question bank.

Question 1

What is $\int_{\sqrt{2}}^{\sqrt{3}} f(x)\,dx$ equal to?

$\sqrt{3} - \sqrt{2}$$2(\sqrt{3} - \sqrt{2})$$3 - \sqrt{2}$$1$

Question 2

What is $\int_n^{n+1}(x - [x])\,dx$, where $[\cdot]$ is the greatest integer function and $n$ is a natural number?

$\dfrac{4n+1}{2}$$\dfrac{2n+1}{2}$$\dfrac{1}{2}$$1$

Question 3

If $\displaystyle\int \sqrt{1 - \sin 2x}\,dx = A\sin x + B\cos x + C$, where $0 < x < \dfrac{\pi}{4}$, then which one of the following is correct?

$A + B = 0$$A + B - 2 = 0$$A + B + 2 = 0$$A + B - 1 = 0$

Question 4

What is $|U^2(x) - V^2(x)|$ equal to?

$0$$1$$2$$3$

Question 5

What is $\int y\,dx$ equal to?

$-\tan(x/2) + c$$-\cot(x/2) + c$$\tan(x/2) + c$$\cot(x/2) + c$

Source Base