Background of Definite Integrals

Definite Integrals are calculated by subtracting the function values of upper and lower limits.
$$\displaystyle \int_{a}^{b}{f(x)}dx = F(a) – F(b), \text{where } \frac{d}{dx}F(x) = f(x)$$

Practice Questions

Question 1

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

Question 2

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

Question 3

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

Question 4

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

Question 5

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