What is the integral from-1 to 2 of 3e^{4x+2} ?

The integral from-1 to 2 of 3e^{4x+2} is (3(e^{12}-1))/(4e^2)

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integral from-1 to 2 of 3e^{4x+2}

\int_{- 1}^{2} 3 e^{4 x + 2} d x

\frac{3 ( e ^{12} - 1 )}{4 e ^{2}}

Decimal Notation

16519.74784 \dots

Solution steps

\int_{- 1}^{2} 3 e^{4 x + 2} d x

Take the constant out:

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

= 3 \cdot \int_{- 1}^{2} e^{4 x + 2} d x

Apply u-substitution

: \int_{- 2}^{10} e^{u} \frac{1}{4} d u

= 3 \cdot \int_{- 2}^{10} e^{u} \frac{1}{4} d u

Take the constant out:

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

= 3 \cdot \frac{1}{4} \cdot \int_{- 2}^{10} e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{4} [e^{u}]_{- 2}^{10}

Simplify

3 \cdot \frac{1}{4} [e^{u}]_{- 2}^{10} : \frac{3}{4} [e^{u}]_{- 2}^{10}

= \frac{3}{4} [e^{u}]_{- 2}^{10}

Compute the boundaries:

e^{10} - \frac{1}{e ^{2}}

= \frac{3}{4} (e^{10} - \frac{1}{e ^{2}})

Simplify

= \frac{3 ( e ^{12} - 1 )}{4 e ^{2}}

\int_{1}^{2} x x + 3 d x

\int_{0}^{2} x \frac{x}{2} d x

\int_{4}^{3} (sin (x)) d x

\int_{0}^{1} 2^{x} \cdot 3^{x} d x

\int_{0}^{1} x 33 x^{2} + 16 d x

What is the integral from-1 to 2 of 3e^{4x+2} ?
The integral from-1 to 2 of 3e^{4x+2} is (3(e^{12}-1))/(4e^2)