Differentiation under Integral Sign
Trending Questions
Q. ∫2π−2πsin6x(sin6x+cos6x)(1+e−x)dx=
- 2π
- π
- π2
- 4π
Q. If f is strictly increasing and positive function, such that xx∫0(1−t)sin(f(t))dt=2x∫0tsin(f(t))dt, where x>0. Then the value of f′(x)cotf(x)+31+x in the domain of f(x) is
Q. If f is continuous function and F(x)=∫x0((2t+3)∫2tf(u)du)dt, then the value of ∣∣∣F′′(2)f(2)∣∣∣
- 9
- 3
- 5
- 7
Q. If f(x) is differentiable and ∫t20xf(x)dx=25t5, then f(425) equals
- 1
- 25
- −52
- 52
Q.
The value of limx→01x3∫x0tln(1+t)t4+4dt is
0
112
124
16
Q. limx→π4∫sec2x2f(t)dtx2−π216equals
- 8πf(2)
- 2πf(12)
- 4f (2)
- 2πf(2)
Q. Let f:R→R be a differentiable function having f(2)=6, f′(2)=(148). Then limx→2∫f(x)64t3x−2dt equals
- 18
- 24
- 12
- 36
Q.
The value of ∫sin2x0sin−1(√t)dt+∫cos2x0cos−1(√t)dt is
0
None of these
π4
π2
Q. If x=∫y0 dt√1+9t2 and d2ydx2= ay, then the value of a is equal to
Q. Let f(x)=∫x1 √2−t2 dt. Then the real roots of the equation x2−f(x)=0 are
- 1
- −1
- 0
- 12
- −12