Draw a picture. We're integrating 2*x* from *a* to 1. Since the integral value is negative there must be some area below the *x*-axis, so we can assume *a* is negative. This line forms two triangles. We know the dimensions of the one above the *x*-axis: The area of the triangle above the *x*-axis is 1. For the triangle below the *x*-axis, we can say what its dimensions are in terms of *a*. Since *a* is negative, the base of the triangle is the positive distance -a. Similarly, the height of the triangle is -2*a*. The area of this triangle is We now have This is a perfectly reasonable equation that we can solve for *a*. Since we know *a* needs to be negative, *a* = -3 is the answer. |