Problem

Given that $ \displaystyle \int^{\pi}_0 \sin ^4x …

01:38

Problem 41 Easy Difficulty

Evaluate $ \displaystyle \int^1_1 \sqrt{1 + x^4}\, dx $.

Name: evaluate displaystyle int1_1 sqrt1 x4 dx
Uploaded: 2021-01-22
Duration: 1 min 48 s
Channel: Numerade
Description: Evaluate $ \displaystyle \int^1_1 \sqrt{1 + x^4}\, dx $.

Answer

0

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Video Transcript

All right, we are going to answer the question. What is the value of one integration from 1 to 1? The square root of one plus X to the fourth the X. Okay, I already know the answer. It only takes half a second to solve this thing. But why can I do that? It's actually based on this idea. The area between the curve and the X axis is written like this. Okay, so one of the first properties that you can see right away is that if the area under the curve it's on Lee from a T A f m x dx, it really doesn't matter what f of X is equal to. So if I try to grow, graph it. Let's say that I have a drawing like this. I started a and I end at a So what's the area under the curve off the line that has, with of zero. Well, I don't know what the height is going to be. I meant I don't know what the function is going to be, but ffx is gonna have ah, height f of A and Delta X is equal to zero. So the area it's just zero because it's f of eight times zero. Okay, So what is this equal to zero? What is this equal to? Well, from 1 to 1, the area under the curve, regardless of what this guy is, has to be zero. And that's how you answer this question.

Yuki H.

University of California, Berkeley

Topics

Integrals

Integration

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 2

The Definite Integral

Problem

Given that $ \displaystyle \int^{\pi}_0 \sin ^4x …

Problem 41 Easy Difficulty

Evaluate $ \displaystyle \int^1_1 \sqrt{1 + x^4}\, dx $.

Answer

0

More Answers

Topics

Calculus: Early Transcendentals

Discussion

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Watch More Solved Questions in Chapter 5

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Grace H.

Anna Marie V.

Kayleah T.

Michael J.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos