Question

Find the area (in square units) of the region under the graph of the function f on the interval [−1, 3].

Answer 1

Answer:

$A = 26$

Step-by-step explanation:

The area of the region under the graph is determined by the following definite integral:

$A = \int\limits^{3}_{-1} {2\cdot x + 4} \, dx$

$A = 2\int\limits^{3}_{-1} {x} \, dx + 4 \int\limits^{3}_{-1} \, dx$

$A = 2 \cdot \left(\frac{x^{2}}{2} \right)|\limits^{3}_{-1} + 4\cdot x |\limits^{3}_{-1}$

$A = 3^{2}-(-1)^{2} + 4\cdot [3-(-1)]$

The area under the function is:

$A = 26$