Chapter 4: Q. 44 (page 405)

Combining derivatives and integrals: Simplify each of the following as much as possible:
$\frac{d}{d x} \int_{0}^{x} e^{- t^{2}} d t$

Short Answer

Expert verified

The derivative of given function is $e^{- x^{2}} .$

Step by step solution

Step 1. Given information

The derivative is-

$\frac{d}{d x} \int_{0}^{x} e^{- t^{2}} d t$

Step 2. Calculation

The derivative is $\frac{d}{d x} \int_{0}^{x} e^{- t^{2}} d t$

Now, if $f$ is continuous on $[a, b]$ then for all $x \in [a, b]$

$\frac{d}{d x} \int_{a}^{x} f (t) d t = f (x) S o, f (t) = e^{- t^{2}} f (x) = e^{- x^{2}}$

The derivative expression can be written as,

$\frac{d}{d x} \int_{0}^{x} e^{- t^{2}} d t = e^{- x^{2}} [f (x) = e^{- x^{2}}]$

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Combining derivatives and integrals: Simplify each of the following as much as possible:
$\frac{d}{d x} \int_{0}^{x} e^{- t^{2}} d t$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Combining derivatives and integrals: Simplify each of the following as much as possible:
$\frac{d}{d x} \int_{0}^{x} e^{- t^{2}} d t$