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

Working definition of continuity , "Working" definition of continuity ...

"Working" definition of continuity A function is continuous in an interval if we can draw the graph from beginning point to finish point without ever once picking up our penci

The mean value theorem with proof, The Mean Value Theorem  Assume f(x)...

The Mean Value Theorem  Assume f(x) is a function that satisfies both of the subsequent. 1.   f(x) is continuous on the closed interval [a,b]. 2.   f(x) is differentiabl

Territories never was a venitian possesion, Which of those territories neve...

Which of those territories never was a Venitian possesion? Cyprus Morea Crete Sicily

Hyperbolic paraboloid- three dimensional space, Hyperbolic Paraboloid- Thre...

Hyperbolic Paraboloid- Three Dimensional Space The equation which is given here is the equation of a hyperbolic paraboloid. x 2 / a 2 - y 2 / b 2 = z/c Here is a dia

Local maxima, Given that f(x,y) = 3xy -  x 2 y  - xy 2 . Fi nd all the poin...

Given that f(x,y) = 3xy -  x 2 y  - xy 2 . Fi nd all the points on the surface z = f(x, y)where local maxima, local minima, or saddles occur

Differentiate functions f ( x ) = 15x100 - 3x12 + 5x - 46, Differentiate f...

Differentiate following functions. (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 (b) h ( x ) = x π   - x √2  Solution (a)    f ( x ) = 15x 100 - 3x 12 + 5x - 46 I

What is the cost to generate, The production costs per week for generating ...

The production costs per week for generating x widgets is given by, C ( x ) = 500 + 350 x - 0.09 x 2 ,         0 ≤ x ≤ 1000 Answer following questions.  (a) What is the c

Calculus level 2, the first question should be done using the website given...

the first question should be done using the website given (www.desmos.com/calculator )and another good example to explain using the graph ( https://www.desmos.com/calculator/ydimzr

Alzebra, how can i memorize the formulas

how can i memorize the formulas

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