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

Area problem, Area Problem Now It is time to start second kind of inte...

Area Problem Now It is time to start second kind of integral: Definite Integrals.  The area problem is to definite integrals what tangent & rate of change problems are to d

The Bake Sale, Lindy has 48 chocolate chip cookies and 64 vanilla wafer coo...

Lindy has 48 chocolate chip cookies and 64 vanilla wafer cookies. How many bags can Lindy fill if she puts the chocolate chip cookies and the vanilla wafers in the same bag? She pl

Fiancial project, With your current loan, explain how much additional money...

With your current loan, explain how much additional money you would need to add to your monthly payment to pay off your loan in 20 years instead of 25. Decide whether or not it wou

Lower than average, A local police precinct has seen a recent enhance in th...

A local police precinct has seen a recent enhance in the number of complaints filed regarding how officers are interacting with the public. Before addressing the issue, the command

Learning to count in maths, Here we learn: 1) Discussed what counting me...

Here we learn: 1) Discussed what counting means, and stressed that it is not the ability to recite number names. 2) Talked about the need for a child to understand several pr

Inequalities, I want to complete my assignment, please explain me what is I...

I want to complete my assignment, please explain me what is Inequalities?

Law of Sine and Cosine Word Problems, A poll tilts towards the sun at an 8 ...

A poll tilts towards the sun at an 8 o angle from the vertical at it casta 22-ft shadow. The angle of elevation from the shadow to the top of the pole is 43 o . How tall is th

Pre-calculus, finding the vertex for the function of the form f(x)=ax^2+bx...

finding the vertex for the function of the form f(x)=ax^2+bx+c

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