Home
Class 12
MATHS
int(a)^(b) f(x) dx =...

`int_(a)^(b) f(x) dx = `

A

`2int_(a)^(b)f(x)dx`

B

`int_(a)^(b)f(a-x)dx`

C

`int_(a)^(b)f(b-x)dx`

D

`int_(a)^(b)f(a+b-x)dx`.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF INTEGRATION

    PREMIERS PUBLISHERS|Exercise Answer the following questions.|18 Videos
  • APPLICATIONS OF INTEGRATION

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISES 9.10|20 Videos
  • APPLICATIONS OF DIFFERENTIAL CALCULUS

    PREMIERS PUBLISHERS|Exercise Problems For Practice (Answer the following question)|39 Videos
  • APPLICATIONS OF MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (II. Answer the following)|15 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(2a) f(x) dx = 0 if ……… .

If int_(0)^(2a) f (x) dx = 2 int_(0)^(a) f(x) then

If f(a+b-x)=f(x) , then int_(a)^(b)xf(x)dx is equal to

If int_(0)^(a) f(x) dx + int_(0)^(a) f(2a-x) dx =

If f(x) is even then int_(-a)^(a)f(x)dx ….

Let the definite integral be defined by the formula int_(a)^(b)f(x)dx=(b-a)/2(f(a)+f(b)) . For more accurate result, for c epsilon (a,b), we can use int_(a)^(b)f(x)dx=int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx=F(c) so that for c=(a+b)/2 we get int_(a)^(b)f(x)dx=(b-a)/4(f(a)+f(b)+2f(c)) . If f''(x)lt0 AA x epsilon (a,b) and c is a point such that altcltb , and (c,f(c)) is the point lying on the curve for which F(c) is maximum then f'(c) is equal to

For every function f (x) which is twice differentiable , these will be good approximation of int_(a)^(b)f(x)dx=((b-a)/(2)){f(a)+f(b)} , for more acutare results for cin(a,b),F( c) = (c-a)/(2)[f(a)-f( c)]+(b-c)/(2)[f(b)-f( c)] When c= (a+b)/(2) int_(a)^(b)f(x)dx=(b-a)/(4){f(a)+f (b)+2 f ( c) }dx If lim_(t toa) (int_(a)^(t)f(x)dx-((t-a))/(2){f(t)+f(a)})/((t-a)^(3))=0 , then degree of polynomial function f (x) atmost is

If y=f(x) is a monotonic function in (a,b), then the area bounded by the ordinates at x=a, x=b, y=f(x) and y=f(c)("where "c in (a,b))" is minimum when "c=(a+b)/(2) . "Proof : " A=int_(a)^(c) (f(c)-f(x))dx+int_(c)^(b) (f(c))dx =f(c)(c-a)-int_(a)^(c) (f(x))dx+int_(a)^(b) (f(x))dx-f(c)(b-c) rArr" "A=[2c-(a+b)]f(c)+int_(c)^(b) (f(x))dx-int_(a)^(c) (f(x))dx Differentiating w.r.t. c, we get (dA)/(dc)=[2c-(a+b)]f'(c)+2f(c)+0-f(c)-(f(c)-0) For maxima and minima , (dA)/(dc)=0 rArr" "f'(c)[2c-(a+b)]=0(as f'(c)ne 0) Hence, c=(a+b)/(2) "Also for "clt(a+b)/(2),(dA)/(dc)lt0" and for "cgt(a+b)/(2),(dA)/(dc)gt0 Hence, A is minimum when c=(a+b)/(2) . The value of the parameter a for which the area of the figure bounded by the abscissa axis, the graph of the function y=x^(3)+3x^(2)+x+a , and the straight lines, which are parallel to the axis of ordinates and cut the abscissa axis at the point of extremum of the function, which is the least, is

PREMIERS PUBLISHERS-APPLICATIONS OF INTEGRATION-PROBLEMS FOR PRACTICE (CHOOSE THE CORRECT ANSWER) :
  1. The volume of solid obtained by revolving (x^2)/(9)+(y^2)/(16)=1 about...

    Text Solution

    |

  2. int(0)^((pi)/( 4)) cos^(3) 2x dx = "….........."

    Text Solution

    |

  3. The value of int(0)^(pi) sin^(4) x dx is

    Text Solution

    |

  4. int(0)^((pi)/(2)) e^(2x) cos xdx is :

    Text Solution

    |

  5. int(0)^((3)/(2)) sqrt(9-4x^2)dx=.

    Text Solution

    |

  6. int(0)^((pi)/(2)) sin^7 xdx is :

    Text Solution

    |

  7. The area of the region bounded by y=x^2-5x+4,x=2,x=3 and the x axis is...

    Text Solution

    |

  8. Find the area of the region bounded by x^2=36y y axis y=2 and y=4.

    Text Solution

    |

  9. Find the common area of x^2=y and y^2 =x.

    Text Solution

    |

  10. int(-2)^(2)(2-x)^2dx is :

    Text Solution

    |

  11. The volume of the solid formed by revolving the area of the circle x^2...

    Text Solution

    |

  12. The volume generated by the region bounded by the curve y=sqrt(x) and ...

    Text Solution

    |

  13. The volume generated by rotating the triangle with vertices (0,0),(4,0...

    Text Solution

    |

  14. The area bounded by y=cos x -sin x between x=0 and x=pi is :

    Text Solution

    |

  15. The volume of solid obtained by revolving the curve y=sec x between x=...

    Text Solution

    |

  16. The plane region bounded by the curve y=sqrt(cosx), 0 le x le (pi)/(2)...

    Text Solution

    |

  17. int(a)^(b) f(x) dx =

    Text Solution

    |

  18. If int(0)^(a) f(x) dx + int(0)^(a) f(2a-x) dx =

    Text Solution

    |

  19. The area between x^2=4-y and the lines y=0,y=3 is :

    Text Solution

    |

  20. The volume of a spherical cap of height (a)/(2) cut off from the spher...

    Text Solution

    |