In the following exercises, verify each identity using differentiation. Then, using the indicated u-substitution, identify f such that the integral takes the form ∫ f ( u ) d u . 260. ∫ x ( 4 x 2 + 9 ) 2 d x = − 1 8 ( 4 x 2 + 9 ) ; u = 4 x 2 + 9
In the following exercises, verify each identity using differentiation. Then, using the indicated u-substitution, identify f such that the integral takes the form ∫ f ( u ) d u . 260. ∫ x ( 4 x 2 + 9 ) 2 d x = − 1 8 ( 4 x 2 + 9 ) ; u = 4 x 2 + 9
In the following exercises, verify each identity using differentiation. Then, using the indicated u-substitution, identify f such that the integral takes the form
∫
f
(
u
)
d
u
.
260.
∫
x
(
4
x
2
+
9
)
2
d
x
=
−
1
8
(
4
x
2
+
9
)
;
u
=
4
x
2
+
9
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.
Let f(x)=sin(2x+4). Which function g(x) represents f shifted two units to the right and one unit downwards?
write the function ?
a) Use the Product Rule to find the derivative of the given function.
b) Find the derivative by multiplying the expressions first.
y = (5Vx +6)x?
a) Use the Product Rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice.
O A. The derivative is (
Vx.
O B. The derivative is (5/x +6)
+
OC. The derivative is (5/x +6) (
O D. The derivative is (5/x +6) x² +
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY