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

5th grade, 6 and 3/8 minus 1 and 3/4

6 and 3/8 minus 1 and 3/4

Longer- term forecasting, Longer- Term Forecasting Moving averages, ex...

Longer- Term Forecasting Moving averages, exponential smoothing and decomposition methods tend to be utilized for short to medium term forecasting. Longer term forecasting is

What is the formula to know total area square shaped quilt, Cathy is formin...

Cathy is forming a quilt out of fabric panels that are 6 in through 6 in. She needs to know the total area of her square-shaped quilt. Which formula will she use? The area of a

Differential equation, Suppose a fluid (say, water) occupies a domain D? R^...

Suppose a fluid (say, water) occupies a domain D? R^(3 ) and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid

Evaluate the volume and surface area of a rectangular solid, Evaluate the v...

Evaluate the volume and surface area of a rectangular solid: Calculate the volume & surface area of a rectangular solid along with a =   3", b = 4", & c = 5".  Solution:

Rate of change interpretation of derivative, Rate of Change : The first in...

Rate of Change : The first interpretation of derivative is rate of change.  It was not the primary problem which we looked at in the limit chapter, however it is the most signific

Find a maximum flow and a minimum cut, Use the maximum flow algorithm to fi...

Use the maximum flow algorithm to find a maximum flow and a minimum cut in the given network, where the capacities of arc CF, EC , DE and BD are w = 13, x = 7, y =1, a

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

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

Number and operations, 1a.if the williams spend $385 a month on food what i...

1a.if the williams spend $385 a month on food what is their monthly income

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