Evaluate the definite integral.

${\int}_{0}^{1}\frac{7}{1+{x}^{2}}dx$

ArcactCatmedeq8
2021-11-19
Answered

Evaluate the definite integral.

${\int}_{0}^{1}\frac{7}{1+{x}^{2}}dx$

You can still ask an expert for help

Parminquale

Answered 2021-11-20
Author has **17** answers

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

$\int}_{0}^{1}\frac{7}{1+{x}^{2}}dx=7{\left[{\mathrm{tan}}^{-1}\left(x\right)\right]}_{0}^{1$

$=7\times \frac{\pi}{4}$

$=\frac{7\pi}{4}$

Refer to the question, we have to solve the definite integral a=0 and b=1

Step 2

Use the formula of integration of arctanx (x) to solve the provided integral

Then

Oung1985

Answered 2021-11-21
Author has **16** answers

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.

$\frac{7\pi}{4}$

Step 2: In this case,

Step 3: SInce

Step 4: Simplify.

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