Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Stuck on your homework problem? This step-by-step video should help.

Try Numerade Free for 30 Days

Like

Report

Solve the given problems by integration.Find the first-quadrant area bounded by $y=2^{x}$ and $x=3 .$ See Exercise 37.

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 3

The Exponential Form

Integrals

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

06:34

Find the area of the follo…

02:12

Find the area of the regio…

02:29

03:33

06:19

Geometry problems Use a ta…

01:33

Find the area under the cu…

04:08

00:54

Find the given area.Th…

01:44

10:00

Okay, so we're finding the area in the first quadrant. So I'm just going to draw a graph of the first quadrant. So it has to be in this first quadrant, which means we're gonna be bounded below by the X. Axis and bounded to the left by the y axis. And that it also said that we're bounded by X is equal to three and also by the function why is equal to to raise the power of X? So that's gonna be a function that looks something I don't know, like I'll draw it a little bit better, something like that. And so the area that we're looking at is going to be Founded by X Equal to three, bounded by our curve, bounded by the Y axis or the X. Axis, and bounded by the Y axis as well. We're bounded by both axis is since we want the first quadrant. So the area is just going to be this shaded in region here. So that's just the integral from 0 to 3 of our function. Y is equal to to raise the power vax. So can now find this integral. So we're doing the integral From 0 to 3 of our function to raise the power of X. Dx. So here the integral of to raise the power of X. Well, it's the anti derivative and we know the derivative of to raise the power of X is just to raise the power of X times the natural log of two. So the integral of to the X is going to be equal to To to the x divided by the natural log of two. Since now, if he found the derivative of this function, we would have to to the X multiplied by the natural log of two, divided by the natural log of two. Which would give us to to the X. Which is our original function. So we're looking at this function to V. X divided by the natural log of two from 0 to 3. So then we have, when X is equal to three is equal to two to the third, divided by the natural log of two, And when X is equal to zero, this is just equal to one, divided by the natural log of two. And so we can plug this into a calculator and two to the third is equal to eight. So we have eight divided by the natural log of two minus one, divided by the natural log of two, which is equal to 10 .099. She can simplify around a little bit, just 10.1.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Find the area of the following regions.The region in the first quadrant …

Find the area of the region in the first quadrant bounded on theleft by …

Find the area of the region described in the following exercises.The reg…

Find the area of the region in the first quadrant bounded on the left by the…

Geometry problems Use a table of integrals to solve the following problems.<…

Find the area under the curve $y=\frac{1}{(x+1)^{3 / 2}}$ bounded on the lef…

Find the given area.The area of the region bounded by $y=x^{3}, x=3$ and…

Find the area of the region in the first quadrant bounded by the line $$y=x,…

Find the area of the region in the first quadrant bounded by theline $y=…

03:21

Give the proper trigonometric substitution and find the transformed integral…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.