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

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

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

\int_{- l n (4)}^{0} 3 e^{x} d x

\frac{3 3}{4}

Decimal

1.29903 \dots

Solution steps

\int_{- l n (4)}^{0} 3 e^{x} d x

Take the constant out:

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

= 3 \cdot \int_{- l n (4)}^{0} e^{x} d x

Use the common integral:

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

= 3 [e^{x}]_{- l n (4)}^{0}

Simplify

ln (4) : 2 ln (2)

= 3 [e^{x}]_{- 2 l n (2)}^{0}

Compute the boundaries:

\frac{3}{4}

= 3 \frac{3}{4}

Simplify

= \frac{3 3}{4}

2 cos (x) + cos^{2} (x)

\int 9 x^{2} + 1 d x

\int \frac{1}{x ^{2} - 4 x - 12} d x

\frac{20}{s ( s ^{2} + 4 )}

\int \frac{1}{1 + cos ( 3 x )} d x

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