Step by step solution to "Evaluate the definite integral. ∫0171+x2dx"

ArcactCatmedeq8

Answered question

2021-11-19

Evaluate the definite integral.

\int_{0}^{1} \frac{7}{1 + x^{2}} d x

Parminquale

Beginner2021-11-20Added 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} d x

\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}} d x = \tan^{- 1} (x)

Then

\int_{0}^{1} \frac{7}{1 + x^{2}} d x = 7 {[\tan^{- 1} (x)]}_{0}^{1}

= 7 \times \frac{π}{4}

= \frac{7 π}{4}

Oung1985

Beginner2021-11-21Added 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 (x) d x = F (x) ∣_{a}^{b} = F (b) - F (a)

Step 2: In this case,

f (x) = \frac{7}{1 + x^{2}}

. Find its integral.

7 \tan^{- 1} (x) ∣_{0}^{1}

Step 3: SInce

F (x) ∣_{a}^{b} = F (b) - F (a)

, expand the above into F(1)−F(0):

7 \tan^{- 1} (1) - 7 \tan^{- 1} (0)

Step 4: Simplify.

\frac{7 π}{4}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?