Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side. ∫ ( 8 x 3 + 1 2 x 2 ) d x = 2 x 4 − 1 2 x + C
Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side. ∫ ( 8 x 3 + 1 2 x 2 ) d x = 2 x 4 − 1 2 x + C
Solution Summary: The author explains the formula used to prove the statement 'displaystyle int' — the derivative of a function is given as nxn-1.
Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side.
∫
(
8
x
3
+
1
2
x
2
)
d
x
=
2
x
4
−
1
2
x
+
C
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.
Calculus 11th Edition - Ron Larson
Chapter 3.9 - Differentials
Find the tangent line approximationT to the graph of f at the given point. Thencomplete the table.
integral calculus: integration
Determining Differentiability In Exercises85–88, find the derivatives from the left and fromthe right at x = 1 (if they exist). Is the functiondifferentiable at x =1?
\text { 8. } f(x)=(1-x)^{2 / 3}
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