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