# Evaluate the definite integral. \int_{0}^{1}\frac{7}{1+x^{2}}dx

Evaluate the definite integral.
${\int }_{0}^{1}\frac{7}{1+{x}^{2}}dx$
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Parminquale
Step 1
Refer to the question, we have to solve the definite integral a=0 and b=1 $\frac{7}{1}+{x}^{2}dx$.
${\int }_{0}^{1}\frac{1}{1+{x}^{2}}$
Step 2
Use the formula of integration of arctanx (x) to solve the provided integral
$\int \frac{1}{1+{x}^{2}}dx={\mathrm{tan}}^{-1}\left(x\right)$
Then
${\int }_{0}^{1}\frac{7}{1+{x}^{2}}dx=7{\left[{\mathrm{tan}}^{-1}\left(x\right)\right]}_{0}^{1}$
$=7×\frac{\pi }{4}$
$=\frac{7\pi }{4}$
###### Not exactly what you’re looking for?
Oung1985
Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:
${\int }_{a}^{b}f\left(x\right)dx=F\left(x\right){\mid }_{a}^{b}=F\left(b\right)-F\left(a\right)$
Step 2: In this case, $f\left(x\right)=\frac{7}{1+{x}^{2}}$. Find its integral.
$7{\mathrm{tan}}^{-1}\left(x\right){\mid }_{0}^{1}$
Step 3: SInce $F\left(x\right){\mid }_{a}^{b}=F\left(b\right)-F\left(a\right)$, expand the above into F(1)−F(0):
$7{\mathrm{tan}}^{-1}\left(1\right)-7{\mathrm{tan}}^{-1}\left(0\right)$
Step 4: Simplify.
$\frac{7\pi }{4}$