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Popular >

integral from 7 to 8 of e^{7-x}

Solution

\int_{7}^{8} e^{7 - x} d x

Solution

1 - \frac{1}{e}

+1

Solution steps

\int_{7}^{8} e^{7 - x} d x

Apply u-substitution

: \int_{0}^{- 1} - e^{u} d u

= \int_{0}^{- 1} - e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{0} - e^{u} d u

Take the constant out:

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

= - (- \int_{- 1}^{0} e^{u} d u)

Use the common integral:

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

= - (- [e^{u}]_{- 1}^{0})

Simplify

= [e^{u}]_{- 1}^{0}

Compute the boundaries:

1 - \frac{1}{e}

= 1 - \frac{1}{e}

Popular Examples

derivative of sin(2)

\frac{d}{d x} (sin (2))

integral of 2xsqrt(x^2+1)

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

2y^{''}-54y=0,y(1)=1,y(2)=2

2 y^{^{''}} - 54 y = 0, y (1) = 1, y (2) = 2

limit as x approaches 0 of x(ln(x))

x \to 0 lim (x (ln (x)))

integral from 0 to 4 of x^2

\int_{0}^{4} x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from 7 to 8 of e^{7-x} ?
The integral from 7 to 8 of e^{7-x} is 1-1/e