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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
- If f(x) is an odd function defined on [-T//2,T//2] and has period T, t...
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- If for every integer n, int(n)^(n+1) f(x)dx=n^(2), then the value of ...
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- int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to
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- The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is
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- The value of int(-1)^(1) x|x|dx, is
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- int0^3 |x^(3)+x^(2)+3x|dx is equal to
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- The value of the integral int(0)^(3) (dx)/(sqrt(x+1)+sqrt(5x+1)) is
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- int(1)^(-1) (x^(3)+|x|+1)/(x^(2)+2|x|+1)dxis equal to
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- int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx...
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- For any natural number n, the value of the integral int(0)^(sqrt(n))...
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- For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...
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- If phi'(x)=(log(e )|sin x|)/(x),x ne pi,n in Z and int(1)^(3) (3log(...
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- The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...
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- Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x i...
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- The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is
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- int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value
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- If [.] denotes the greatest integer function and f(x)={:{(3[x]-(5|x|...
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- Find the value of int(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denot...
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- The value of int(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int(-1)^(1) cos^(-...
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- Let Delta(y)=|{:(y+a,y+b,y+a-c),(y+b,y+c,y-1),(y+c,y+d,y-b+d):}| and,...
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