Q. 21 - Calculus

Question

Use geometry (i.e., areas of triangles, rectangles, and circles) to find the exact values of each of the definite integrals in Exercises $21-28$.

${\int }_0^2(2-x)dx$.

Step-by-Step Solution

Answer

The exact value of ${\int }_0^2(2-x)dx$ is, $2$.

Step 1 . Given information

${\int }_0^2(2-x)dx$.

Step 2 . The following figure shows the graph of 2 - x .

Step 3 . Find the area.

The area of the shaded region is,

$\frac{1}{2}\times 2\times 2=2$

Therefore, the exact value is, $2$.