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

Rlc circuit, State clearly that the current in an RLC circuit with an AC so...

State clearly that the current in an RLC circuit with an AC source with and without the use of complex variables

Two consecutive positive integers whose product is 90, What is the lesser o...

What is the lesser of two consecutive positive integers whose product is 90? Let x = the lesser integer and let x + 1 = the greater integer. Because product is a key word for m

Calculate the price of the horseracing track, There are five horseracing tr...

There are five horseracing tracks in Kentucky. The Kentucky legislature allows only one track to be open at a time. How does this restriction affect the price the track can charge

Area of the equilateral triangle, Area of the equilateral triangle: ...

Area of the equilateral triangle: Given : D, E, F are the mind points of BC, CA, AB. R.T.P. : We have to determine the ratio of the area of of triangle DEF and triangle AB

Poisson mathematical properties, Poisson Mathematical Properties 1. Th...

Poisson Mathematical Properties 1. The expected or mean value = np = λ Whereas; n = Sample Size p = Probability of success 2. The variance = np = ? 3. Standard dev

How much does it car cost her per year, Ashley's car insurance costs her $1...

Ashley's car insurance costs her $115 per month. How much does it cost her per year? Multiply $115 by 12 because there are 12 months in a year; $115 × $12 = $1,380 per year.

Trigonometric ratios, How do you find the ratio for these problems?

How do you find the ratio for these problems?

Example of vector, Provide the vector for each of the following. (a) The...

Provide the vector for each of the following. (a) The vector from (2, -7, 0) -  (1, - 3, - 5 ) (b) The vector from (1,-3,-5) - (2, - 7, 0) (c) The position vector for ( -

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