- #1

- 347

- 2

## Homework Statement

Evaluate:

A:

[tex]

\int^{16}_0 (\sqrt{x} - 1)\,dx

[/tex]

B:

[tex]

\int^4_1 \frac{2}{\sqrt{x}}\,dx

[/tex]

C:

[tex]

\int^6_2 \frac{4}{x^3}\,dx

[/tex]

## Homework Equations

n/a

## The Attempt at a Solution

Its part C which I think I have done wrong, but the others could be too.

Part A:

[tex]

\int^{16}_0 (\sqrt{x} - 1)\,dx = \int^{16}_0 (x^{\frac{1}{2}}-1)\,dx = [\frac{2}{3}x^{1.5}-1x]^{16}_0 = [112]-[0] = 112 \,sq\, units

[/tex]

Part B:

[tex]

\int^4_1 \frac{2}{\sqrt{x}}\,dx = \int^4_1 2x^{-\frac{1}{2}}\,dx = [4x^{\frac{1}{2}}]^4_1 = [8] - [4] = 4 \,sq\, units

[/tex]

C:

[tex]

\int^6_2 \frac{4}{x^3}\,dx = \int^6_2 4x^{-3}\,dx = [-2x^{-2}]^6_2 = [-\frac{1}{18}] - [-\frac{1}{2}] = 0.44 \,sq\, units

[/tex]

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