/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 38 Use the Second Fundamental Theor... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 38 (page 399)

Use the Second Fundamental Theorem of Calculus, if needed, to calculate each of the derivatives given below.

ddx鈭�0x鈥�e鈭�t2dt

Short Answer

Expert verified

Ans: ddx鈭�0x鈥�e鈭�t2dt=e-x2

Step by step solution

01

Step 1. Given information.

given,

ddx鈭�0x鈥�e鈭�t2dt

02

Step 2. The objective is to calculate the derivative.

Now, if fis continuous on [a,b]then for all x鈭�[a,b],

ddx鈭�ax鈥�f(t)dt=f(x)

So,

f(t)=e鈭�t2f(x)=e鈭�x2

03

Step 3. The derivative expression can be written as,

ddx鈭�0x鈥�e鈭�t2dt=e鈭�x2f(x)=e鈭�x2

Therefore, the answer is e-x2.

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

Most popular questions from this chapter

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: tanx=sinxcosx).

鈭�x2x3+15dx.

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value.

limn鈫�鈭�鈭�k=1nk2+k+1n

Write out all the integration formulas and rules that we know at this point.

Describe an example that illustrates that 鈭�ab|f(x)|dx is not equal to |鈭�abf(x)dx|.

Describe the intervals on which the function f is positive, negative, increasing and decreasing. Them describe the intervals on which the function A is positive , negative, increasing and decreasing
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.