- #1
FaraDazed
- 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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