Barrons AP Calculus - David Bock
(E) The integral equals it is equivalent to where u = 1 − ln t. ...
(A) Replace u by x in the given integral to avoid confusion in applying the Parts Formula. To integrate let the variable u in t ...
(D) The integral is equivalent to Use formula (4) on the first integral and (18) on the second. ...
(D) The integral is equivalent to Use formula (17) on the first integral. Rewrite the second integral as and use (3). ...
(E) Rewrite: ...
(B) Hint: Divide, getting ...
(D) Letting u = sin θ yields the integral Use formula (18). ...
(E) Use integration by parts, letting u = arctan x and dv = dx. Then The Parts Formula yields ...
(B) Hint: Note that Or multiply the integrand by recognizing that the correct answer is equivalent to −ln|e−x − 1|. ...
(D) Hint: Expand the numerator and divide. Then integrate term by term. ...
(C) Hint: Observe that e2 ln u = u^2. ...
(A) Let u = 1 + ln y^2 = 1 + 2 ln |y|; integrate ...
(B) Hint: Expand and note that Use formulas (9) and (7). ...
(E) Multiply by The correct answer is tan θ − sec θ + C. ...
(D) Note the initial conditions: when t = 0, v = 0 and s = 0. Integrate twice: v = 6t^2 and s = 2 t^3. Let t = 3. ...
(D) Since y ′ = x^2 − 2, Replacing x by 1 and y by −3 yields ...
(D) When t = 0, v = 3 and s = 2, so v = 2t + 3t^2 + 3 and s = t^2 + t^3 + 3t + 2. Let t = 1. ...
(C) Let then v = at + C. (*) Since v = 75 when t = 0, therefore C = 75. Then (*) becomes v = at + 75 so 0 = at + 75 and a = −1 ...
(A) Divide to obtain Use partial fractions to get ...
Answers Explained (C) The integral is equal to ...
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