What is the integral from 0 to 3 of 450.268e^{1.12567t} ?

The integral from 0 to 3 of 450.268e^{1.12567t} is 11313.23346…

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integral from 0 to 3 of 450.268e^{1.12567t}

\int_{0}^{3} 450.268 e^{1.12567 t} d t

11313.23346 \dots

Solution steps

\int_{0}^{3} 450.268 e^{1.12567 t} d t

Take the constant out:

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

= 450.268 \cdot \int_{0}^{3} e^{1.12567 t} d t

Apply u-substitution

: \int_{0}^{3.37701} e^{u} \frac{1}{1.12567} d u

= 450.268 \cdot \int_{0}^{3.37701} e^{u} \frac{1}{1.12567} d u

Take the constant out:

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

= 450.268 \cdot \frac{1}{1.12567} \cdot \int_{0}^{3.37701} e^{u} d u

Simplify

= 450.268 \cdot 0.88835 \dots \cdot \int_{0}^{3.37701} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 450.268 \cdot 0.88835 \dots [e^{u}]_{0}^{3.37701}

Simplify

= 400 [e^{u}]_{0}^{3.37701}

Compute the boundaries:

28.28308 \dots

= 400 \cdot 28.28308 \dots

Simplify

= 11313.23346 \dots

x \to \infty lim (e^{x} - x)

\int \frac{x ^{2} + 1}{x ^{4} + 1} d x

2 e^{x} cos (x)

\frac{\partial}{\partial x} (ln (x^{3}))

\int \frac{1}{( 1 - y )} d y

What is the integral from 0 to 3 of 450.268e^{1.12567t} ?
The integral from 0 to 3 of 450.268e^{1.12567t} is 11313.23346…