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f(x)=45/(1+x^2)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫0∞(451+x2)dx\int_0^{\infty}\left(\frac{45}{1+x^2}\right)dx

Step-by-step Solution

Learn how to solve problems step by step online. Integrate the function 45/(1+x^2) from 0 to infinity. The integral of a function times a constant (45) is equal to the constant times the integral of the function. Solve the integral by applying the formula \displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right). Add the initial limits of integration. Replace the integral's limit by a finite value.
Integrate the function 45/(1+x^2) from 0 to infinity

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Final answer to the exercise

45π2\frac{45\pi }{2}

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∫0∞(451+x2 )dx
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