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Hello student, The given integral is Let I = We know So I = Adding (1) and (2) we get 2I = 2I = 2π So I = π.
Fundamental theorem : The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.
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Hi, This one is very simple. Whate ever is inside the root, you need to bring x in negetive power. So take x^4 common from the root. When it comes out of root it will become x^3 and the x^2 already...
integral mod(x)= 1/2(x 2 ).sgn(x)
Hi, I think there is some probl;em with the image u uploaded. Please upload the image again to get solution !
Factorise the denominator. Partial fractions and then integration by standard results.
Solve all these using integration by parts
I found a simpler way to solve this ,than integration by parts.
Hi, This is a Homogeneous differential equation. So put y=vx and solve, ie keeping v as avariable find dv/dx in terms of dy/dx and substitute also substitute the value of y in the expression. Upon...
I = ∫ (3x 3 -5x 2 +4x-9)dx / (x 2 +2) = ∫ (3x-5)dx + ∫ (-2x+1)dx / (x 2 +2) [Simple division] = 3x 2 /2 – 5x – ∫ 2xdx / (x 2 +2) + ∫ dx / (x 2 +2) = 3x 2 /2 – 5x – log|x 2 +2| + 1/rt(2)*tan -1...
log x 2 = 2 logx and integration of logx is =xlogx – x,,using ILATE so the answer is 2(xlogx -x)