What is the integral from 3 to 9 of 20e^{-0.1t^2} ?

The integral from 3 to 9 of 20e^{-0.1t^2} is 10.06967…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 3 to 9 of 20e^{-0.1t^2}

\int_{3}^{9} 20 e^{- 0.1 t^{2}} d t

10.06967 \dots

Solution steps

\int_{3}^{9} 20 e^{- 0.1 t^{2}} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 20 \cdot \int_{3}^{9} e^{- 0.1 t^{2}} d t

= 20 \cdot \int_{3}^{9} e^{- (0.1 t)^{2}} d t

Apply u-substitution

: \int_{0.94868 \dots}^{2.84604 \dots} e^{- u^{2}} \frac{1}{0.31622 \dots} d u

= 20 \cdot \int_{0.94868 \dots}^{2.84604 \dots} e^{- u^{2}} \frac{1}{0.31622 \dots} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 20 \cdot \frac{1}{0.31622 \dots} \cdot \int_{0.94868 \dots}^{2.84604 \dots} e^{- u^{2}} d u

Simplify

= 20 \cdot 3.16227 \dots \cdot \int_{0.94868 \dots}^{2.84604 \dots} e^{- u^{2}} d u

Use the nonelementary integral:

\int e^{- u^{2}} d u = \frac{π}{2} erf (u)

= 20 \cdot 3.16227 \dots [\frac{π}{2} erf (u)]_{0.94868 \dots}^{2.84604 \dots}

Simplify

= 63.24555 \dots [0.88622 \dots erf (u)]_{0.94868 \dots}^{2.84604 \dots}

Compute the boundaries:

0.15921 \dots

= 63.24555 \dots \cdot 0.15921 \dots

Simplify

= 10.06967 \dots

\int_{- \infty}^{\frac{π}{2}} tan (θ) d θ

\int_{1}^{6} 3 x - 2 d x

\int_{1}^{2} \frac{7}{x} d x

\int_{0}^{2} \frac{x}{4 x + 1} d x

\int_{2}^{5} 2 x^{2} - x - 1 d x

What is the integral from 3 to 9 of 20e^{-0.1t^2} ?
The integral from 3 to 9 of 20e^{-0.1t^2} is 10.06967…