Home
Class 12
MATHS
Let f(x)=|[secx,cosx,sec^2x+cotxcosecx],...

Let `f(x)=|[secx,cosx,sec^2x+cotxcosecx],[cos^2x,cos^2x,cosec^2x],[1,cos^2x,cos^2x]|` Prove that `int_0^(pi/2)f(x)dx=-pi/4-8/(15)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,cos^2x,cos^2x]| then, int_-pi^(pi)f(x)dx equals

f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,cos^2x,cos^2x)| then int_0^(pi/2) f(x) dx=.....

Prove that : int_(0)^(pi) x cos^(2) x dx =(pi^(2))/(4)

Let f(x)= |{:(cosx,sinx,cosx),(cos2x,sin2x,2cos2x),(cos3x,sin3x,3cos3x):}| then find the value of f'((pi)/(2)) .

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Evaluate int_0^pi x/(a^2-cos^2x)dx

Let f(x)=|(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0)| . Then the value of int_0^(pi//2)[f(x)+f^(prime)(x)]dx is a. pi b. pi//2 c. 2pi d. 3pi//2

int_(0)^(pi//2) x^(2) cos x dx

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Let f(x)=|(cos x,e^(x^2) , 2x cos^2x/2),(x^2, sec x, sinx+x^3),(1,2,x+tan x)| then the value of int_(-pi/2)^(pi/2)(x^2+1)(f(x)+f''(x))dx

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If Deltar=|[2^(r-1) , 2.3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 ,...

    Text Solution

    |

  2. Find a quadratic polynomial phi(x) whose zeros are the maximum and mi...

    Text Solution

    |

  3. Let f(x)=|[secx,cosx,sec^2x+cotxcosecx],[cos^2x,cos^2x,cosec^2x],[1,co...

    Text Solution

    |

  4. Show that: |[a,b-c,c+b],[a+c,b,c-a],[a-b,b+a,c]|=(a+b+c)(a^2+b^2+c^2).

    Text Solution

    |

  5. If a , b , c are real numbers, prove that |[a,b,c],[b,c,a],[c,a,b]|=-(...

    Text Solution

    |

  6. Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0

    Text Solution

    |

  7. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

    Text Solution

    |

  8. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

    Text Solution

    |

  9. Solve : |[x-2,2x-3,3x], [-4x-4,2x-9,3x-16], [x-8,2x-27,3x-64]| = 0

    Text Solution

    |

  10. If x+y+z=0 , prove that |[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y ...

    Text Solution

    |

  11. If a , b , c are all positive and are pth ,qth and rth terms of a G.P....

    Text Solution

    |

  12. Prove that: |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-...

    Text Solution

    |

  13. |[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|...

    Text Solution

    |

  14. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

    Text Solution

    |

  15. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

    Text Solution

    |

  16. Prove that: |[a, b, ax+by],[ b, c, bx+cy], [ax+by, bx+cy,0]|=(b^2-a c)...

    Text Solution

    |

  17. Without expanding the determinant, show that (a+b+c) is a factor of th...

    Text Solution

    |

  18. If m in N and mgeq2, prove that: |1 1 1m(C1)m+1(C1)m+2(C1)m(C2)m+1(C2...

    Text Solution

    |

  19. Evaluate: =|(10 !, 11 !, 12 !), (11 !, 12 !, 13 !), (12 !, 13 !, 14 !)...

    Text Solution

    |

  20. Show that: |b+c c+a a+b q+r r+p p+q y+z z+x x+y|=2|a b c p q r x y z|

    Text Solution

    |