What is the integral from-1 to 1 of e^y-(y^2-7) ?

The integral from-1 to 1 of e^y-(y^2-7) is e-1/e+40/3

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integral from-1 to 1 of e^y-(y^2-7)

\int_{- 1}^{1} e^{y} - (y^{2} - 7) d y

e - \frac{1}{e} + \frac{40}{3}

Decimal

15.68373 \dots

Solution steps

\int_{- 1}^{1} e^{y} - (y^{2} - 7) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{1} e^{y} d y - \int_{- 1}^{1} y^{2} - 7 d y

\int_{- 1}^{1} e^{y} d y = e - \frac{1}{e}

\int_{- 1}^{1} y^{2} - 7 d y = - \frac{40}{3}

= e - \frac{1}{e} - (- \frac{40}{3})

Simplify

= e - \frac{1}{e} + \frac{40}{3}

\frac{d}{d x} (lo g_{9} (- (x - 4) (5 x - 2)))

\frac{\partial}{\partial y} (sin (x) y)

f (x) = \frac{x ^{5} + x ^{9}}{x}

y = 8 e^{- x} + e^{3 x}

x \to 0 lim (1 - \frac{cos ( x )}{x})

What is the integral from-1 to 1 of e^y-(y^2-7) ?
The integral from-1 to 1 of e^y-(y^2-7) is e-1/e+40/3