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

Solve the value of x and y , 7(y + 3) - 2(x + 2) = 14, 4 (y - 2) + 3(x ...

7(y + 3) - 2(x + 2) = 14, 4 (y - 2) + 3(x - 3) = 2 Ans:    7(y + 3) - 2 (x+ 2) = 14          --------- (1) 4(y- 2) + 3(x - 3) = 2 ----------(2) From (1) 7y +21 -

Three times the larger of the two numbers, If three times the larger of the...

If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is

Objectives of why learn mathematics, Objectives After studying this uni...

Objectives After studying this unit, you should be able to explain how mathematics is useful in our daily lives; explain the way mathematical concepts grow; iden

Calculate the probability, Data collected from the STATS 10x class survey o...

Data collected from the STATS 10x class survey one semester included responses to questions on the number of different sexual partners and on the number of pairs of shoes the stude

Calculus (The squeeze theorem), When finding the limit as x approaches 0 th...

When finding the limit as x approaches 0 the for function (square root of x^3 + x^2) cos(pi/2x) would the limit not exist because there would be a zero in the denominator?

#mathematics induction, how many numbers must be selected from the set A={1...

how many numbers must be selected from the set A={1, 3, 5, 7, 9, 11, 13, 15}to guarantee that at least one pair of these numbers add up to16? Explain and justify your answer

Find the quadratic polynomial, Find the Quadratic polynomial whose sum and ...

Find the Quadratic polynomial whose sum and product of zeros are √2 + 1, 1/ √2 + 1 Ans:    sum = 2  √2 Product = 1 Q.P = X 2 - (sum) x + Product ∴ x 2 - (2 √2 )

Tutor, How to be an expert at expertsmind

How to be an expert at expertsmind

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