To help find the velocity of particles requires the evaluation of the indefinite integral of the acceleration function, a(t), with respect to time, t, i.e. v = [ a(t)dt. Evaluate the following indefinite integrals. Check your value for each integral by differentiating your answer. (a) 5t (8 cos 2t64 sin 4t + 27e¯³t)dt; (b) √(324t5 - 54t² + 5)(Int)² dt;

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 7E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...
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To help find the velocity of particles requires the evaluation of the indefinite integral
of the acceleration function, a(t), with respect to time, t, i.e.
v =
·
Evaluate the following indefinite integrals.
= √ a(t)dt.
Check your value for each integral by differentiating your answer.
(a)
5t (8 cos 2t64 sin 4t + 27e¯³t)dt;
(b)
√(324t5 - 54t² + 5)(Int)² dt;
Transcribed Image Text:Question To help find the velocity of particles requires the evaluation of the indefinite integral of the acceleration function, a(t), with respect to time, t, i.e. v = · Evaluate the following indefinite integrals. = √ a(t)dt. Check your value for each integral by differentiating your answer. (a) 5t (8 cos 2t64 sin 4t + 27e¯³t)dt; (b) √(324t5 - 54t² + 5)(Int)² dt;
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(c)
S
(d)
5t8-3 sin 6t+4e-6t
42+ 10t9+9 cos 6t- 12e-6t
15e6t-3e3t-504
dt;
(e3t+3)(e³t+7)
dt;
Transcribed Image Text:(c) S (d) 5t8-3 sin 6t+4e-6t 42+ 10t9+9 cos 6t- 12e-6t 15e6t-3e3t-504 dt; (e3t+3)(e³t+7) dt;
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