Suppose \( f(x) \) and \( g(x) \) are two continuous functions defined for \( 0 \leq x \leq 2 \)... VIDEO
Suppose \( f(x) \) and \( g(x) \) are two continuous functions defined for \( 0 \leq x \leq 2 \). Given \( f(x)=\int_{0}^{1} e^{x+t} \cdot f(t) d t \) and \( g(x)=\int_{0}^{1} e^{x+t} \cdot g(t) d t+x \)
The value of \( g(0)-f(0) \) equals :
(a) \( \frac{2}{3-e^{2}} \)
(b) \( \frac{3}{e^{2}-2} \)
(c) \( \frac{1}{e^{2}-1} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2022-10-27 Let \( z \) be a complex number of constant modulus such that \( z^{2} \) is purely imaginary th... 2022-10-27 \( x^{3 m}+x^{3 n-1}+x^{3 r-2} \), where \( m, n, r, \in N \), is divisible by
(a) \( x^{2}-x+1 ... 2022-10-27 For \( a0 \), find the minimum value of the integral \( \int_{0}^{1 / a}\left(a^{3}+4 x-a^{5} x^... 2022-10-27 Suppose \( f(x) \) and \( g(x) \) are two continuous functions defined for \( 0 \leq x \leq 2 \)... 2022-10-27 The equation \( x^{3 / 4\left(\log _{2} x\right)^{2}+\log _{2} x-5 / 4}=\sqrt{2} \) has
(a) at l... 2022-10-27 If the maximum value of the expression \( y=\frac{x^{4}-x^{2}}{x^{6}+2 x^{3}-1} \) for \( x1 \),... 2022-10-27 Let a solution \( y=y(x) \) of the differential equation, \( d y+x y d x=x d x \) satisfy \( y(0... 2022-10-27 If \( \lim _{x \rightarrow a} f(x)=\lim _{x \rightarrow a}[f(x)](a \) is a finite quantity), whe... 2022-10-27 Let \( \frac{x d y}{d x}-y=x^{2}\left(x e^{x}+e^{x}-1\right) \) for all \( x \in R-\{0\} \) such... 2022-10-27 Solution of the differential equation \( \left(e^{x^{2}}+e^{y^{2}}\right) y \frac{d y}{d x}+e^{x... 2022-10-27 Suppose \( f(x) \) and \( g(x) \) are two continuous functions defined for \( 0 \leq x \leq 2 \)... 2022-10-27 The set of value(s) of ' \( a \) ' for which the function \( f(x)=\frac{a x^{3}}{3}+(a+2) x^{2}+... 2022-10-27 The absolute value of \( \frac{\int_{0}^{\pi / 2}(x \cos x+1) e^{\sin x} d x}{\int_{0}^{\pi / 2}... 2022-10-27 If \( a \) and \( b \) are any two vectors, then possible integers(s) in the range of \( \frac{3... 2022-10-27 Locus of the point \( z \) satisfying the equation \( |i z-1|+|z-1|=2 \), is (where, \( i=\sqrt{... 2022-10-27 If \( (\alpha, \beta) \) be an end of a diagonal of a square and the other diagonal has the equa... 2022-10-27 Which of the following is/are correct?
(1) \( (\tan x)^{\ln (\sin x)}(\cot x)^{\ln (\sin x)}, \f... 2022-10-27 If \( \cos \alpha=\frac{1}{2}\left(x+\frac{1}{x}\right) \) and \( \cos \beta=\frac{1}{2}\left(y+... 2022-10-27 For \( 0\phi\pi / 2 \), if \( x=\sum_{\infty}^{\infty} \cos ^{2 n} \phi, y=\sum_{n=0}^{\infty} \... 2022-10-27 If each of the vertices of a triangle has integral coordinates then the triangle may be
(a) righ... 2022-10-27 If the tangent to the ellipse \( x^{2}+4 y^{2}=16 \) at the point \( P(\theta) \) is a normal to...