What is the integral from-1 to 5 of sqrt(2x+6)-x+1 ?

The integral from-1 to 5 of sqrt(2x+6)-x+1 is 38/3

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integral from-1 to 5 of sqrt(2x+6)-x+1

\int_{- 1}^{5} 2 x + 6 - x + 1 d x

\frac{38}{3}

Decimal

12.66666 \dots

Solution steps

\int_{- 1}^{5} 2 x + 6 - x + 1 d x

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}^{5} 2 x + 6 d x - \int_{- 1}^{5} x d x + \int_{- 1}^{5} 1 d x

\int_{- 1}^{5} 2 x + 6 d x = \frac{56}{3}

\int_{- 1}^{5} x d x = 12

\int_{- 1}^{5} 1 d x = 6

= \frac{56}{3} - 12 + 6

Simplify

\frac{56}{3} - 12 + 6 : \frac{38}{3}

= \frac{38}{3}

\int_{- 2}^{3} (9 - x^{2}) - (3 - x) d x

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\int_{3}^{7} x^{2} lo g_{10} (x) d x

\int_{6}^{9} (\frac{1}{x ^{2}}) d x

\int_{- 3}^{0} 9 - x^{2} d x

What is the integral from-1 to 5 of sqrt(2x+6)-x+1 ?
The integral from-1 to 5 of sqrt(2x+6)-x+1 is 38/3