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

Complex Numbers, How do you compute the phase/angle of a complex number? i....

How do you compute the phase/angle of a complex number? i.e 1+2i

Strategy for series - sequences and series, Strategy for Series Now t...

Strategy for Series Now that we have got all of our tests out of the way it's time to think regarding to the organizing all of them into a general set of strategy to help us

Find out the minimum distance from the origin, Problem 1. Find the maximum...

Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c

Determinarte, what is the differeance in between determinate and matrix .

what is the differeance in between determinate and matrix .

Probability, A card is chosen at random from a pack of playing cards.what i...

A card is chosen at random from a pack of playing cards.what is d probability that it is either a heart or the queen of spades

Relative measures of dispersion, Relative measures of dispersion Defi...

Relative measures of dispersion Definition of Relative measures of dispersion: A relative measure of dispersion is a statistical value that may be utilized to compare va

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.

Examples of elimination technique - linear algebra, Explain some examples o...

Explain some examples of Elimination technique of Linear Equations.

Tangents, find a common tangent to two circles

find a common tangent to two circles

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