Cracking The Ap Calculus ab Exam 2018

1 − x^2 = 1 − x x^2 − x = 0 x(x − 1) = 0 x = 0, 1 The left-hand edge of the region is ...

Notice that cos x is on top between 0 and , then sin x is on top between and . The point where they ...

(cos x − sin x) dx = (sin x − cos x) (sin x − cos x) dx = (−cos x − sin x) Adding th ...

3. First, sketch the region. When you slice up the area horizontally, the right end of each section is the c ...

From x = −3 to x = 0, if you slice the region vertically, the curve y = is on top, and the x-ax ...

limits to y-limits. The two curves intersect at y = , so our limits of integration are from y = 0 to ...

Because the curve y = 3 − x^2 is always above y = 1 − x within the interval, you have to eval ...

Because the curve crosses the x-axis at , you have to divide the region into two parts: from x = 0 to ...

You don’t have the endpoints this time, so you need to find where the two curves intersect. If you set ...

Next, find where the two curves intersect. By setting y^3 − y = 0, you’ll find that they intersec ...

3.The curve y = x^2 − 4x − 5 and the curve y = 2x − 5. 4.The curve y = x^3 and the x-axi ...

Chapter 17 The Volume of a Solid of Revolution ...

Does the chapter title leave you in a cold sweat? Don’t worry. You’re not alone. This chapter covers a to ...

= πx Each disk is infinitesimally thin, so its thickness is dx; if you add up the volumes of all the disks ...

When you slice vertically, the top curve is y = x and the limits of integration are from x = 0 to x ...

If you slice this region vertically, each cross-section looks like a washer (hence the phrase ...

π[f(x)^2 − g(x)^2 ] To find the volume, evaluate the integral. π [f(x)^2 − g(x)^2 ] dx This is the formul ...

Suppose the region we’re interested in is revolved around the y-axis instead of the x-axis. Now, to find the vol ...

π (y^4 − y^6 ) dx = π There’s only one more nuance to cover. Sometimes you’ll have to revolve the region ...

π [4x + 2)^2 − (x^2 + 2)^2 ] dx Suppose instead that the region was revolved about the line x = − ...