Problem 15

Question

Find the indefinite integral and check your result by differentiation. $$ \int d u $$

Step-by-Step Solution

Verified

Answer

The indefinite integral of du is $u + C$, where $C$ is the constant of integration.

1Step 1: Compute Indefinite Integral

The given function is $\int du$ which means an integral with respect to $u$. The integral of $du$ is simply $u$, as the integral of $1$ with respect to $u$ is $u$. So the antiderivative $F(u) = u + C$, where C is the constant of integration.

2Step 2: Check the result by differentiation

In order to check if the computed antiderivative is correct, differentiate it with respect to $u$. The derivative of $u$ is $1$ and the derivative of a constant is $0$. Therefore, $F'(u) = 1 + 0 = 1$. Thus, the differentiation result checks out with the original function.

Problem 15

Problem 16

Other exercises in this chapter

Problem 15

Use the Log Rule to find the indefinite integral. $$ \int \frac{1}{3-2 x} d x $$

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Problem 15

Find the indefinite integral and check the result by differentiation. $$ \int 2 x\left(x^{2}-1\right)^{7} d x $$

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Problem 16

Use the Midpoint Rule with $n=4$ to approximate the area of the region bounded by the graph of $f$ and the $x$ -axis over the interval. Compare your resul

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Problem 16

Sketch the region bounded by the graphs of the functions and find the area of the region. $$ y=x^{3}-2 x+1, y=-2 x, x=1 $$

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