Statement 1: If the primitive of f(x)=pi...

Statement 1: If the primitive of `f(x)=pisinpix+2x-4` has the value `-2` for `x=1,` then there are exactly two values of `x` for which primitive of `f(x)` vanishes. Statement 2: `cospix` has period 2.

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Each question contains statements given in two columns which have to b...
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The value of ∫e^2x ( 1/x − 1/(2x^2) )dx is
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Statement 1: If the primitive of f(x)=pisinpix+2x-4 has the value -2 f...
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Let f(x)=2^(2x−1)and ϕ(x) =−2^x+2xlog2. If f'(x)>ϕ'(x), then value of ...
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Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-...
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If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b...
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If f(x)=int(3x^2+1)/((x^2-1)^3)dx and f(0)=0, then the value of |2/(f(...
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Evaluate: intsqrt((1-sqrt(x))/(1+sqrt(x)))dx
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"If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c...
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The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...
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Let f(x)=int(x^2dx)/((1+x^2)(1+sqrt(x^2+1)))a n df(0)=0. Then value o...
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If y=intsqrt(x)(1+x^(1/3))^4dx is equal to
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If intsqrt(1+sinx)f(x)dx=2/3(1+sinx)^(3/2)+c ,t h e nf(x)e q u a l co...
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Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is
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Evaluate:∫x⋅sqrt(1−x^4)dx
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