Q. 31 Use the Second Fundamental Theor... [FREE SOLUTION]

Chapter 4: Q. 31 (page 399)

Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31鈥�34.
$f (x) = \sin^{2} (3^{x})$

Short Answer

Expert verified

The three antiderivatives for the function $f (x) = \sin^{2} (3^{x})$ are $F (x) = {鈭�}_{- 1}^{x} \sin^{2} (3 t) d t, F (x) = {鈭�}_{1}^{x} \sin^{2} (3 t) d t, F (x) = {鈭�}_{2}^{x} \sin^{2} (3 t) d t$ .

Step by step solution

Step 1. Given Information.

The function:

$f (x) = \sin^{2} (3^{x})$

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 $F (x) = {鈭�}_{a}^{x} f (t) . d t$ for all $x 鈭� [a, b]$ .

So, $F (x) = {鈭�}_{- 1}^{x} \sin^{2} (3 t) d t$ is defined to be an anti-derivative of the given function.

Similarly, the other two anti-derivatives are:

$F (x) = {鈭�}_{1}^{x} \sin^{2} (3 t) d t, F (x) = {鈭�}_{2}^{x} \sin^{2} (3 t) d t$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31鈥�34.
$f (x) = \sin^{2} (3^{x})$

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

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Mechanics Maths

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31鈥�34.f(x)=sin2(3x)

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

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Mechanics Maths

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Use the Second Fundamental Theorem of Calculus to write down three antiderivatives of each function fin Exercises 31鈥�34.
$f (x) = \sin^{2} (3^{x})$