(a)If [.] denotes the greatest integer function and (p)1 f(x)={3[x]−5|x|x; x≠0 2;x=0 then ∫2−32f(x)dx is equal to (b)The value of∫π2−π2cos x1+exdx is(q)−112(c)If I1=∫sinθ1x1+x2dx and I2=∫cscθ11x(x2+1)dx then(r)9the value of∣∣∣∣∣I1I21I2eI1+I2I21−11I21+I22−1∣∣∣∣∣(d)Let f(x) be a polynomial of degree 2 satisfying(s)0 f(0)=1,f′(0)=−2 and f′′(0)=6,then∫2−1f(x)dx is equal to

(a)If [.] denotes the greatest integer function and (p)1 f(x)={3[x]−

1.	(a)If [.] denotes the greatest integer function and (p)1 f(x)={3[x]−5\|x\|x; x≠0 2;x=0 then ∫2−32f(x)dx is equal to (b)The value of∫π2−π2cos x1+exdx is(q)−112(c)If I1=∫sinθ1x1+x2dx and I2=∫cscθ11x(x2+1)dx then(r)9the value of∣∣∣∣∣I1I21I2eI1+I2I21−11I21+I22−1∣∣∣∣∣(d)Let f(x) be a polynomial of degree 2 satisfying(s)0 f(0)=1,f′(0)=−2 and f′′(0)=6,then∫2−1f(x)dx is equal to
Answer» $\begin{matrix} (a) & If [.] denotes the greatest integer function and & (p) & 1 f (x) = {\begin{matrix} 3 [x] - \frac{5 \| x \|}{x}; x \neq 0 2; x = 0 \end{matrix} then \int_{\frac{- 3}{2}}^{2} f (x) d x is equal to (b) & The value of \int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{c o s x}{1 + e^{x}} d x is & (q) & - \frac{11}{2} (c) & If I_{1} = \int_{1}^{sin θ} \frac{x}{1 + x^{2}} d x and I_{2} = \int_{1}^{csc θ} \frac{1}{x (x^{2} + 1)} d x then & (r) & 9 the value of ∣ ∣∣∣ ∣ \begin{matrix} I_{1} & I_{1}^{2} & I_{2} e^{I_{1} + I_{2}} & I_{1}^{2} & - 1 1 & I_{1}^{2} + I_{2}^{2} & - 1 \end{matrix} ∣ ∣∣∣ ∣ (d) & Let f (x) be a polynomial of degree 2 satisfying & (s) & 0 f (0) = 1, f^{'} (0) = - 2 and f^{''} (0) = 6, then \int_{- 1}^{2} f (x) d x is equal to \end{matrix}$