Topic

Definite Integrals

Topic Progress:


$$ \begin{aligned} \displaystyle \int_{a}^{b}{x^n}dx &= \Big[\dfrac{x^{n+1}}{n+1}\Big]_{a}^{b} \\ &= \dfrac{b^{n+1}}{n+1} - \dfrac{a^{n+1}}{n+1} \end{aligned} $$

Practice Questions

Question 1

Evaluate \( \displaystyle \int_{1}^{2}{2x}dx \).

Question 2

Evaluate \( \displaystyle \int_{0}^{2}{6x}dx \).

Question 3

Evaluate \( \displaystyle \int_{2}^{4}5dx\).

Question 4

Evaluate \( \displaystyle \int_{1}^{3}{(2x+4)}dx\).

Question 5

Evaluate \( \displaystyle \int_{0}^{1}{4}dx \).

Question 6

Evaluate \( \displaystyle \int_{1}^{3}{(6x^2 - 10x)}dx \).

Question 7

Evaluate \( \displaystyle \int_{-1}^{2}{(x+2)(x-1)}dx \).

Question 8

Evaluate \( \displaystyle \int_{-1}^{1}{6\sqrt[3]{x}}dx \).

Question 9

Evaluate \( \displaystyle \int_{0}^{1}{\dfrac{1}{\sqrt{3+2x}}}dx \).

Question 10

Evaluate \( \displaystyle \int_{0}^{2}{(2x-1)^3}dx \).

Question 11

Evaluate \( \displaystyle \int_{0}^{1}{(2x-1)^3}dx\).

Question 12

Evaluate \( \displaystyle \int_{-1}^{4}{\sqrt{3x+4}}dx \).

Question 13

Evaluate \( \displaystyle \int_{1}^{3}{\dfrac{x-2}{x^3}}dx \).

Question 14

Evaluate \( \displaystyle \int_{2}^{3}{\dfrac{3}{(2x+3)^2}}dx \).

Question 15

Find \(k\), if \( \displaystyle \int_{2}^{3}{(2x+k)}dx = 9 \).

Question 16

Find \( \displaystyle \dfrac{d}{dx}\int_{3}^{x}{(4t^3-3t^2+2t-1)}dx \).

MD5104