What is the integral from-ln(4) to 0 of 4sqrt(3)e^t ?

The integral from-ln(4) to 0 of 4sqrt(3)e^t is 3sqrt(3)

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integral from-ln(4) to 0 of 4sqrt(3)e^t

\int_{- l n (4)}^{0} 43 e^{t} d t

33

Decimal

5.19615 \dots

Solution steps

\int_{- l n (4)}^{0} 43 e^{t} d t

Take the constant out:

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

= 43 \cdot \int_{- l n (4)}^{0} e^{t} d t

Use the common integral:

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

= 43 [e^{t}]_{- l n (4)}^{0}

Simplify

ln (4) : 2 ln (2)

= 43 [e^{t}]_{- 2 l n (2)}^{0}

Compute the boundaries:

\frac{3}{4}

= 43 \frac{3}{4}

Simplify

= 33

What is the integral from-ln(4) to 0 of 4sqrt(3)e^t ?
The integral from-ln(4) to 0 of 4sqrt(3)e^t is 3sqrt(3)