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

Three person problem of points, Three-person Problem of Points: Pascal, Fer...

Three-person Problem of Points: Pascal, Fermat and their old friend the Chevalier de Mere each put $10.00 into a pot, and agree to play a game that has rounds. Each player has the

Rational exponents, Now we have to start looking at more complicated expone...

Now we have to start looking at more complicated exponents. In this section we are going to be evaluating rational exponents. i.e. exponents in the form

Mensuration, if area of a rectangle is 27 sqmtr and it perimeter is 24 m fi...

if area of a rectangle is 27 sqmtr and it perimeter is 24 m find the length and breath#

Find the total volume of the hay stack, The lower portion of a hay stack is...

The lower portion of a hay stack is an inverted cone frustum and the upper part is a cone find the total volume of the hay stack.

Permutation and combination, howmany numbers made by digit 0,1,2,3,5,7,9 bu...

howmany numbers made by digit 0,1,2,3,5,7,9 but any digit isnot repeted

Parent, Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbl...

Sam has 18 marbles. Dean has 3 marbles. Dean has ---- as many marbles as Sam?

Explain peano''s axioms with suitable example, Question 1 Explain Peano's ...

Question 1 Explain Peano's Axioms with suitable example Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b 2 +1. Find a) (f °g

Matrices, how to find inverse of matrix

how to find inverse of matrix

What is perfect squares, What is Perfect Squares ? Any number that can ...

What is Perfect Squares ? Any number that can be written as an integer to the power of two is called a perfect square. For example, 4 can be written as 2 2 4 is a "perfect sq

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