Chapter 4: Q. 33 (page 399)

Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31–34.
$f (x) = e^{x^{2}}$

Short Answer

Expert verified

The three antiderivatives for the function $f (x) = e^{x^{2}}$ are $F (x) = \int_{- 1}^{x} e^{t^{2}} d t, F (x) = \int_{0}^{x} e^{t^{2}} d t, F (x) = \int_{1}^{x} e^{t^{2}} d t$ .

Step by step solution

Step 1. Given Information.

The function:
$f (x) = e^{x^{2}}$

Step 2. Graph the function.

Graph the function.

Step 3. Find the anti-derivatives.

If F is an anti-derivative of f,f is continuous on [a,b], then $F (x) = \int_{a}^{x} f (t) . d t$ for all $x \in [a, b]$ .

So, $F (x) = \int_{- 1}^{x} e^{t^{2}} d t$ is defined to be an anti-derivative of the given function.

Similarly, the other two anti-derivatives are:

$F (x) = \int_{0}^{x} e^{t^{2}} d t, F (x) = \int_{1}^{x} e^{t^{2}} d t$ .

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Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31–34.
$f (x) = e^{x^{2}}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the function.

Step 3. Find the anti-derivatives.

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Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31–34.f(x)=ex2

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the function.

Step 3. Find the anti-derivatives.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Decision Maths

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31–34.
$f (x) = e^{x^{2}}$