In the following exercises, evaluate the indefinite integral ∫f(x)dx with constant C=0 using u-substitution. Then, graph the function and the antiderivative over the indicated interval. If possible, estimate a value of C that would need to be added to the antiderivative to make it equal to the definite integral F(x)=∫xa f(t)dt, with a the left endpoint of the given interval. Is the substitution u=1−x^2 in the definite integral 2 ∫ (x / 1 − x^2) dx okay? If not, why not? 0
In the following exercises, evaluate the indefinite integral ∫f(x)dx with constant C=0 using u-substitution. Then, graph the function and the antiderivative over the indicated interval. If possible, estimate a value of C that would need to be added to the antiderivative to make it equal to the definite integral F(x)=∫xa f(t)dt, with a the left endpoint of the given interval. Is the substitution u=1−x^2 in the definite integral 2 ∫ (x / 1 − x^2) dx okay? If not, why not? 0
In the following exercises, evaluate the indefinite integral ∫f(x)dx with constant C=0 using u-substitution. Then, graph the function and the antiderivative over the indicated interval. If possible, estimate a value of C that would need to be added to the antiderivative to make it equal to the definite integral F(x)=∫xa f(t)dt, with a the left endpoint of the given interval. Is the substitution u=1−x^2 in the definite integral 2 ∫ (x / 1 − x^2) dx okay? If not, why not? 0
In the following exercises, evaluate the indefinite integral ∫f(x)dx with constant C=0 using u-substitution. Then, graph the function and the antiderivative over the indicated interval. If possible, estimate a value of C that would need to be added to the antiderivative to make it equal to the definite integral F(x)=∫xa f(t)dt, with a the left endpoint of the given interval.
Is the substitution u=1−x^2 in the definite integral
2
∫ (x / 1 − x^2) dx okay? If not, why not?
0
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.
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