Cracking The Ap Calculus ab Exam 2018

x) dx. Now, we can evaluate the integral: ∫(x − 2 sec^2 x) dx = − 2 tan x + C. SOLUTIONS TO ...

. Now we can integrate: = = . Last, we substitute back and get . 4. If we let u = x^3 + 3x, ...

7. If we let u = , then du = − dx. We need to substitute for dx, so we can divide the du term b ...

The width of each rectangle is found by taking the difference between the endpoints and dividing ...

The width of each rectangle is found by taking the difference between the endpoints and dividing ...

The height of each trapezoid is found by taking the difference between the endpoints and dividing ...

The height of each rectangle is found by taking the difference between the endpoints and dividing ...

Fundamental Theorem of Calculus, dx = . If we evaluate the integral at the limits, we get = . 6. 2 Accord ...

Recall that the formula for finding the area under the curve using the left endpoints is [y 0 + y 1 ...

2. We find the average value of the function, f(x), on the interval [a, b] using the formula f(c) = f(x) ...

f(t) dt = f(x). We get dt = 3 = 27x^2 − 9x. Don’t forget that because the upper limit is a funct ...

3. We find the derivative of the inverse tangent using the formula (tan−1 u) = . Here we have u = ex, ...

Substituting back, we get tan−1 + C. tan−1 (ln x) + C Recall that = tan−1 u + C. Here we ...

SOLUTIONS TO PRACTICE PROBLEM SET 23 ln |tan x| + C Whenever we have an integral in the form of ...

logarithm. A clue is whether the numerator is the derivative of the denominator, as it is in the first inte ...

we need to substitute for x dx, so if we divide du by 10, we get du = x dx. Now, if we substitute into ...

Here we will use the Power Rule, which says that ∫ xn dx = + C. First, let’s simplify the int ...

6. If we let u = x − 1, then du = dx. Next we can substitute into the integral: ∫ = ∫ u−2 du. N ...

The width of each rectangle is found by taking the difference between the endpoints and dividing ...

2 x^3 We find the derivative of an integral using the Second Fundamental Theorem of Calculus: f(t) ...