For the following exercises, evaluate the definite integrals. Express answer in exact form whenever possible. 109. ∫ π / 6 π / 3 cos 3 x sin x d x (Round this answer to three decimal places.)
For the following exercises, evaluate the definite integrals. Express answer in exact form whenever possible. 109. ∫ π / 6 π / 3 cos 3 x sin x d x (Round this answer to three decimal places.)
For the following exercises, evaluate the definite integrals. Express answer in exact form whenever possible.
109.
∫
π
/
6
π
/
3
cos
3
x
sin
x
d
x
(Round this answer to three decimal places.)
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
dx
x² +9
2.
Use an appropriate trigonometric substitution to rewrite J
as
J(a simplified trig function of 0) d0. Carefully show your work
with differentials and use of trig identities to help simplify.
Then find the integral. Show any use of substitutions and reasoning with right triangles.
Use the method of substitution to find the following indefinite integral.
sin (9z-5)dz
J
sin (9z-5)dz
(Use integers or fractions for any numbers in the expression. Use fractional exponents. Use C as an arbitrary constant.
Use Table to evaluate the following definite integrals.
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY