If \( f(x)=A \sin (\pi x / 2)+B, f^{\prime}(1 / 2)=\sqrt{2} \) and \( \int_{0}^{1} f(x) d x=\fra...
If \( f(x)=A \sin (\pi x / 2)+B, f^{\prime}(1 / 2)=\sqrt{2} \) and \( \int_{0}^{1} f(x) d x=\frac{2 A}{\pi} \), then the constants \( A \) and \( B \) are (resp.)
(a) \( \pi / 2, \pi / 2 \)
(b) \( 2 / \pi, 3 \pi \)
(c) \( 0,-4 \pi \)
(d) \( 4 / \pi, 0 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2022-11-19 | The differential equation of parabola with axis parallel to \( y \)-axis and length of latus rec... |
| 2022-11-19 | The degree of the differential equation whose primitive is \( c^{2}+2 c y+a^{2}-x^{2}=0 \), wher... |
| 2022-11-19 | The solution of the equation \( (2 x+y+1) \mathrm{d} x+(4 x+ \) \( 2 y-1) \mathrm{d} y=0 \) is
(... |
| 2022-11-19 | Let \( F(x)=\int_{x^{2}}^{x^{3}} \frac{d t}{\log t}, x0 \). then
(a) \( f^{\prime}(x)=-1 / 6 \lo... |
| 2022-11-19 | The particular solution of \( t\left(1+t^{2}\right) d x=\left(x+x t^{2}-t^{2}\right) d t,\left.x... |
| 2022-11-19 | The absolute value of \( \int_{10}^{19} \frac{\sin x}{1+x^{8}} \mathrm{~d} x \) is
(a) less than... |
| 2022-11-19 | The particular solution of \( \log \frac{\mathrm{d} y}{\mathrm{~d} x}=3 x+4 y, y(0)= \) 0 is
(a)... |
| 2022-11-19 | \( \int_{\pi / 2}^{3 \pi / 2}[2 \sin x] d x \) is equal to \( ([x] \) denotes the greatest integ... |
| 2022-11-19 | If \( I_{1}=\int_{x}^{1} \frac{d t}{1+t^{2}} \) and \( I_{2}=\int_{1}^{1 / x} \frac{d t}{1+t^{2}... |
| 2022-11-19 | If \( \int_{\log 2}^{x} \frac{d x}{\sqrt{e^{x}-1}}=\frac{\pi}{6} \), the value of \( x \) is
(a)... |
| 2022-11-19 | If \( f(x)=A \sin (\pi x / 2)+B, f^{\prime}(1 / 2)=\sqrt{2} \) and \( \int_{0}^{1} f(x) d x=\fra... |
| 2022-11-19 | Let \( f(x) \) and \( g(x) \) be two functions satisfying \( f\left(x^{2}\right)+ \) \( g(4-x)=4... |
| 2022-11-19 | Let \( f(x), g(x) \) and \( h(x) \) be continuous function on \( [0, a] \) such that \( f(x)=f(a... |
| 2022-11-19 | If the primitive of \( \frac{x^{5}+x^{4}-8}{x^{3}-4 x} \) is \( \frac{x^{3}}{3}+\frac{x^{2}}{2}+... |
| 2022-11-19 | If the integrand is a rational function of \( x \) and fractional powers of a linear fractional ... |
| 2022-11-19 | The value of \( \int_{0}^{1}|\sin 2 \pi x| d x \) is equal to
(a) 0
(b) \( -1 / \pi \)
(c) \( 1 ... |
| 2022-11-19 | The value of \( \int_{1 / e^{2}}^{e}|\log x| d x \) is
(a) \( 2\left(1-1 / e^{2}\right) \)
(b) \... |
| 2022-11-19 | The value of \( \int_{0}^{\sin ^{2} x} \sin ^{-1} \sqrt{t} d t+\int_{0}^{\cos ^{2} x} \cos ^{-1}... |
| 2022-11-19 | If \( a \) continuous function \( f \) on \( [0, a] \) satisfy \( f(x) f(a-x)=1, a0 \) then \( \... |
| 2022-11-19 | The value of \( \int_{1}^{e}\left(\frac{\tan ^{-1} x}{x}+\frac{\log x}{1+x^{2}}\right) \mathrm{d... |
| 2022-11-19 | If \( m \neq n, m, n \in \mathbf{N} \), then the value of \( \int_{0}^{2 \pi} \cos m x \cos n x ... |
0