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

Circle, a wheel revolves 360 deegre revolution in one minute .Find how many...

a wheel revolves 360 deegre revolution in one minute .Find how many radians will the wheel subtend in one second

Divides a given line-segment externally in the ratio of 1:2, Divides a give...

Divides a given line-segment externally in the ratio of 1:2 Construction: i )Draw BX making an actueangle at B. ii) Starting from B, mark 2 equal points on BX as shown in the f

Laws of logarithms, express each logariths in terms of log3 P and log3 Q. 1...

express each logariths in terms of log3 P and log3 Q. 1. log3 P^2 Q^3

Determine the probability - probability example, Consider two bags, A and B...

Consider two bags, A and B, with the following contents Bag A Bag B 3 white marbles 4 white marbles 2 red marbles

Normal to y=f(x) , If the normal to y=f(x) makes an angle of pie/4 with y-a...

If the normal to y=f(x) makes an angle of pie/4 with y-axis at (1,1) , then f''(x) is eqivalent to? Ans) The normal makes an angle 135 degree with the x axis. also f ''(1)

Find out all the critical points for the function, Find out all the critica...

Find out all the critical points for the function. Solution To determine the derivative it's probably simple to do a little simplification previous to we in fact diffe

Stats Combination Questions, A car buyer has a choice of three makes, five ...

A car buyer has a choice of three makes, five body styles, and six colors. How many different choices does the buyer have?

Vertical tangent for parametric equations, Vertical Tangent for Parametric ...

Vertical Tangent for Parametric Equations Vertical tangents will take place where the derivative is not defined and thus we'll get vertical tangents at values of t for that we

What is 19% of 26, What is 19% of 26? To ?nd out 19% of 26, multiply 26...

What is 19% of 26? To ?nd out 19% of 26, multiply 26 through the decimal equivalent of 19% (0.19); 26 × 0.19 = 4.94.

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