💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Sketch the region enclosed by the curves and find its area.$$y=\sec ^{2} x, y=2, x=-\pi / 4, x=\pi / 4$$

$$\pi-2$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 6

APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING

Section 1

Area Between Two Curves

Integrals

Integration

Applications of Integration

Area Between Curves

Volume

Arc Length and Surface Area

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:56

Sketch the region enclosed…

01:02

0:00

05:00

04:10

06:22

05:08

02:23

02:13

04:47

Oh, so, uh, the first thing to recognize is that seek it is a reciprocal co sign. So, like, I've had students actually draw out the coastline graph. It was a terrible looking grossing graph, but you could keep it if you want. Um, and co sign seeking is the reciprocal of that. So that's where we get a graph that looks like this. So this is my graph of seeking squared of X, and you'd have one. Um well, it actually be squared. Should be up here as well. Um, but we have these bounds of negative pie or two. Wait, Native pirate four. Excuse me. Um, exit goes negative pie before and positive pi over four. Those air vertical lines and there's one more bound that they give. You know, I don't know exactly where it is, but somewhere on here ah, y equals two. Because this values one, in case you didn't know. So we're looking for this area. So, um what the X values that they gave you? Where were your bounds? Native power for two pi over four. The upper function is y close to, and you want to subtract off the other folks? You Seacon Square to vex the X. I think from here all you have to do is the anti derivative and plug in. I think I'm doing this right. Uh, so what's the anti derivative of two will attach next to it because, remember, the drift of of this needs the equal to and in the same manner. I would just think of what derivative would give me seeking Squared in that answer is tangent. The derivative of tangent is seeking squared. So I'm good from Native Piper for two positive I before. So now we can plug in, Um, we get two times pi over four minus tangent of PIRA for and then minus two times negative pira for you. Plug in your lower around minus tangent of Negative Piper for So let's just look at a unit circle real quick at pyre or four is in the first quadrant where the X and y corner the same. So if you do sign over co sign because of the same values, you get one. So this value equals one. And what happens whether this value will Now that just tells you that we're going into, you know, clockwise. So it's a positive negative, but they're the same coordinates. So this value right here is a negative one. So, what are we looking at? Well, um, to over four reduces of one half. Uh, we're looking at pi over two minus one. A minus. Um, Well, this will turn this into plus pi over two. Same math, um, minus and negative. There would be a plus, but when you distribute that and would be minus one again. So as I'm looking at this, if we add, like terms, we get two pi over two minus two, but he calls in here, and then you could simplify that to just be pi minus two. I'm happy that answer.

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Sketch the region enclosed by the curves and find its area.$$y=\cos …

Sketch the region enclosed by the given curves and find its area.$y=x^{2…

Sketch the region enclosed by the given curves and calculate its area.

Sketch the region enclosed by the given curves and find its area.

$ …

Sketch the region enclosed by the curves and find its area.$$y=x, y=…

Sketch the region enclosed by the curves and find its area.$$x=\sin …

Sketch the region enclosed by the curves and find its area.$$y=x^{3}…