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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
Write the quadratic equation whose roots are real and non conjugate Ans) x^2-x+6=0 ...roots are real and non conjugate
Solve 2 ln (√x) - ln (1 - x ) = 2 . Solution: Firstly get the two logarithms combined in a single logarithm. 2 ln (√x) - ln (x - l) = 2 ln ((√x) 2 ) ln (1 - x ) = 2
Q. What is a Negative Number? Ans. Negative numbers are very important in mathematics. We say that positive and negative numbers are opposites of one another. Here
r=asin3x
x^2-5x+4 can written in roots as (x-1)*(x-4) x^2-4 can be written interms of (x-2)(x+2).so [(x-1)(x-4)/(x-2)(x+2)]
Kara brought $23 with her when she went shopping. She spent $3.27 for lunch and $14.98 on a shirt. How much money does she have left? The two items that Kara bought must be sub
1/cos(x-a)cos(x-b)
Functions and Graphs Need assistance, Please describe Functions and Graphs.
I have difficuties in working out those 3D trigomentry problems within teh shortest possible time. Are there any tricks to get through such problems as soon as possible?
find the no of solution of 2*3*4*5*6*6
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