Final Answer
$\frac{2}{3}$
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Step-by-step Solution
Problem to solve:
$\int_{\frac{1}{2}}^{\frac{3}{4}}\frac{1}{u^2}dx$
Specify the solving method
1
Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$
$\int_{\frac{1}{2}}^{\frac{3}{4}} u^{-2}du$
Learn how to solve definite integrals problems step by step online.
$\int_{\frac{1}{2}}^{\frac{3}{4}} u^{-2}du$
Learn how to solve definite integrals problems step by step online. Integrate the function 1/(u^2) from 1/2 to 3/4. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -2. Evaluate the definite integral. Simplifying.
Final Answer
$\frac{2}{3}$