Related InterviewSolutions

• Evaluate:`int1/(4cos^2x+9sin^2x)dx`
• If `int sqrt(cos^3x/sin^11x) dx = -2(A tan^(9//2)x + B tan^(5//2) x) + C,` then find A and B.A. `A=(1)/(9),B=-(1)/(5)`B. `A=(1)/(9),B=(1)/(5)`C. `A=-(1)/(9),B=(1)/(5)`D. none of these
• `int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx` is equal toA. `log_(e)(tan^(2)x+sqrt(1+tan^(4)x))+C`B. `(1)/(2)log_(e)(tan^(2)x+sqrt(1+tan^(4)x))+C`C. `(1)/(4)log(tan^(2)x+sqrt(1+tan^(4)x))+C`D. none of these
• The value of `int(1-x^7)/(x(1+x^7))dx` is equal toA. `a=1,b=(2)/(7)`B. `a=-1,b=(2)/(7)`C. `a=1,b=-(2)/(7)`D. `a=-1,b=-(2)/(7)`
• `int(x-x^5)^(1/5) / x^6 dx`A. `(5)/(24)((1)/(x^(4))-1)^(6//5)+C`B. `(5)/(24)(1-(1)/(x^(4)))^(6//5)+C`C. `-(5)/(24)(1-(1)/(x^(4)))^(6//5)+C`D. none of these
• Evaluate:`(sin^3x dx)/((cos^4x+3cos^2x+1)tan^(-1)(secx+cosx)`A. `tan^(-1)(secx+cosx)+C`B. `log_(e)|tan^(-1)(secx+cosx)|+C`C. `(1)/((secx+cosx)^(2))+C`D. none of these
• `int(3 sinx+ 2 cos x)/(3 cosx+2 sin x)dx= ax+b log |3cos x + 2 sin x| +C`, then (a ,b)A. `a=(5)/(13), b =-(12)/(13)`B. `a=(12)/(13),b =-(5)/(13)`C. `a=(12)/(13),b=(5)/(13)`D. `a=(-12)/(5),b=(-5)/(13)`
• Let F(x) be an indefinite integral of `sin^(2)x` Statement I The function F(x) satisfies `F(x+pi)=F(x)` for all real x. Because Statement II `sin^(2)(x+pi)=sin^(2)x,` for all real x.A. Statement - 1 True , Statement -2 is True , Statement -2 is a correct explanation for Statement -1.B. Statement - 1 is True , Statement -2 is True , Statement -2 is a correct explanation for Statement -1.C. Statement - 1 True ,Statement - 2 is False.D. Statement - 1 is False , Statement - 2 is True.
• If `intsec^(4//3)c "cosec"^(8//3)x dx =a(tanx)^(-5//3)+b(tanx)^(1//3)+C`, then 5a +b=A. 3B. `-3`C. 0D. `-1`
• The value of `int(sinx +cosx)/(3+sin2x)dx` , isA. `(1)/(4)log((2+sinx - cosx)/(2-sinx+cosx))+C`B. `(1)/(2)log((2+sinx)/(2-sinx))+C`C. `(1)/(4)log((1+sinx)/(1-sinx))+C`D. none of these