Definite integral, Mathematics

Assignment Help:

from 0->1:
Int sqrt(1-x^2)

Solution)

I=∫sqrt(1-x2)dx = sqrt(1-x2)∫dx - ∫{(-2x)/2sqrt(1-x2)}∫dx ---->(INTEGRATION BY PARTS)        = x√(1-x2) - ∫-x2/√(1-x2)

Let I1= ∫x2/√(1-x2) = ∫1-x2-1/√(1-x2) = ∫√(1-x2) - ∫1/√(1-x2) = ∫√(1-x2) - sin-1x = I - sin-1x

I = x√(1-x2) - I + sin-1x

2I = x√(1-x2) + sin-1x

I = x/2*√(1-x2) + 1/2*sin-1x

Within limits 0 -> 1

I = [1/2*√(1-1) + 1/2sin-11 - 1/2*√(1-0) - 1/2sin^-1(0) ] = 0 + pi/2 - 1/2 - 0 =  pi/2 - 1/2

 


Related Discussions:- Definite integral

Velocity of a particle, A particle moves along a straight line so that afte...

A particle moves along a straight line so that after t secs its distance from fixed point O on the line is given by s=(t-1)^2(t-2).find the distance from O when the velocity is zer

Probability, I have a question that hurts my head to work out. It is really...

I have a question that hurts my head to work out. It is really confusing for me. It sais " By the start of the 21st century, only 1 in 6 babies in America was born with blue eyes.

Process for solving linear equations, 1. If the equation has any fractions ...

1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al

Binomial probability distribution, Binomial Probability Distribution B...

Binomial Probability Distribution Binomial probability distribution is a set of probabilities for discrete events. Discrete events are those whose outcomes or results can be c

Example on eulers method, For the initial value problem y' + 2y = 2 - e ...

For the initial value problem y' + 2y = 2 - e -4t , y(0) = 1 By using Euler's Method along with a step size of h = 0.1 to get approximate values of the solution at t = 0.1, 0

Simplification, If 3/5=5,4/7=8,8/7=6 then, what should 9/6 be ?

If 3/5=5,4/7=8,8/7=6 then, what should 9/6 be ?

Differential equations, Find the normalized differential equation which has...

Find the normalized differential equation which has {x, xex} as its fundamental set

Trignometry, verify 4(sin^4 30^0+cos60^0 )-3(cos^2 ?45?^0-sin^2 90^0 )=2

verify 4(sin^4 30^0+cos60^0 )-3(cos^2 ?45?^0-sin^2 90^0 )=2

Shares and dividends, to use newspaperto study and report on shares and div...

to use newspaperto study and report on shares and dividend

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd