Inequalities of Integrals
Trending Questions
Q. 28. Given f(x)=[1/3+x/66], find sum of f(x) for x=1 to 66
Q.
If f and g are two functions over real numbers defined as f(x) = 3x + 1, g(x) = x2 + 2, then find f-g
x2+1-3x
x2+1
3x + x2
3x – x2-1
Q. Let f(x) be positive, continuous, and differentiable on the interval (a, b) and limx→a+f(x)=1, limx→b−f(x)=31/4. If f′(x)≥f3(x)+1f(x), then the greatest value of b−a is
- π48
- π36
- π24
- π12
Q. The area bounded by the curve y = sinx and x-axis between x = 0 and x = π is (in sq. units)
x = 0 तथा x = π के मध्य वक्र y = sinx तथा x-अक्ष द्वारा परिबद्ध क्षेत्र का क्षेत्रफल है (वर्ग इकाई में)
x = 0 तथा x = π के मध्य वक्र y = sinx तथा x-अक्ष द्वारा परिबद्ध क्षेत्र का क्षेत्रफल है (वर्ग इकाई में)
- 1
- 2
- π2
- π
Q. 23. If f(x)= x-1/x+1 , then f(2x) is equal to
Q.
If I=∫π20dx√1+sin3x, then
0<I<1
I>π2√2
I<√2π
I>2π
Q. ∫π0 x sin x1+cos2 xdx=
- π22
- π23
- π2
- π24
Q. 49.: Given that f(x)=X-1, g(x)=X2-2, h(X)=X3-3; Then find 1. fo(goh) 2. (fog)oh
Q. Function f(x)=tanx is discontinuous at-
- x=0
- x=π/2
- x=π
- x=−π
Q. Convert the following products into factorials:
(i) 5 · 6 · 7 · 8 · 9 · 10
(ii) 3 · 6 · 9 · 12 · 15 · 18
(iii) (n + 1) (n + 2) (n + 3) ... (2n)
(iv) 1 · 3 · 5 · 7 · 9 ... (2n − 1)
(i) 5 · 6 · 7 · 8 · 9 · 10
(ii) 3 · 6 · 9 · 12 · 15 · 18
(iii) (n + 1) (n + 2) (n + 3) ... (2n)
(iv) 1 · 3 · 5 · 7 · 9 ... (2n − 1)
Q. For the function Prove that f' (1) = 100 f' (0).
Q. ∫10tan−1(1−x+x2)dx= ___
- In 2
- π4
- π2
- π2−In2
Q. Let f(x), g(x), h(x) be continous in [0, 2a] and satisfies f(2a−x)=f(x), g(2a−x)=g(x), h(x)+h(2a−x)=3, f(2a−x)g(2a−x)=f(x)g(x)then∫2a0f(x)g(x)h(x)dx=
- ∫2a0f(x)g(x)dx
- 3∫a0f(x)g(x)dx
- 2∫a0f(x)g(x)dx
- ∫a0f(x)g(x)dx
Q. ∫π20log(cos x)dx=
- π log 2
- −π2log 2
- −π22 log 2
- none
Q. ∫π20 4 sin x+3 cos xsin x+cos xdx=
- 5π4
- 3π2
- 7π4
- 5π6
Q. 34. let g(x) be a function satisfying g(0)=2, g(1)=3, g(x+2)=2g(x)-g(x+1), then find g(5)
Q. 94. f(x)f(1÷ x)=f(x)+f(1÷ x); and f(3)=-26, find. |f(2)| ?
Q. 21.f(x).f(1/x)=f(x)+f(1/x) gives f(x) = f(1/x)/f(1/x)-1 how?
Q. 17. If f is a function such that f(0) =2, f(1) =3, f(x+2) =2f(x)-f(x+1) then f(5)is
Q. 23. Prove that f:R>R defined as f(x) = x+4x+5 is one one