Notice that it crosses the x-axis at x = −2 and at x = 4.
The formula for the area of the region under the curve f(x) and above the x-axis from x = a to x
= b is f(x) dx.
Thus, in order to find the area of the desired region, we need to evaluate the integral (8 +
2 x − x^2 ) dx.
- D Use the Chain Rule: = sec(πx^2 )tan(πx^2 )(2πx).
- D First, take the derivative: = − (x − 2) , which can be rewritten as . If
we plug in x = 2, we get zero in the denominator so the derivative does not exist at x = 2.
- A This integral is of the form = sin−1 + C, where a = 1.
Thus, we get
