What is the integral from 0 to 4 of 1+sqrt(x) ?

The integral from 0 to 4 of 1+sqrt(x) is 28/3

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integral from 0 to 4 of 1+sqrt(x)

\int_{0}^{4} 1 + x d x

\frac{28}{3}

Decimal

9.33333 \dots

Solution steps

\int_{0}^{4} 1 + x 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_{0}^{4} 1 d x + \int_{0}^{4} x d x

\int_{0}^{4} 1 d x = 4

\int_{0}^{4} x d x = \frac{16}{3}

= 4 + \frac{16}{3}

Simplify

4 + \frac{16}{3} : \frac{28}{3}

= \frac{28}{3}

\int_{1}^{2} \frac{t}{t ^{2} - 1} d t

\int_{1}^{2} 1

\int_{- 2}^{2} 1 - \frac{x ^{2}}{4} d x

\int_{1}^{4} (x^{2} + 6) d x

\int_{3}^{x^{2}} \frac{1}{t ^{4}} d t

What is the integral from 0 to 4 of 1+sqrt(x) ?
The integral from 0 to 4 of 1+sqrt(x) is 28/3