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
Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
In the following exercises, evaluate the indefinite
Is the substitution u=1−x^2 in the definite integral
2
∫ (x / 1 − x^2) dx okay? If not, why not?
0
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