MCQ
$\int {{{13}^x}dx} $ is
- ✓$\frac{{{{13}^x}}}{{\log 13}} + c$
- B${13^{x + 1}} + c$
- C$14x + c$
- D${14^{x + 1}}$+ c
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$( S_{1})$: $2|\hat{ a } \times \hat{ b }|=|\hat{ a }-\hat{ b }|$
$(S_{2})$ : The projection of $\hat{a}$ on $(\hat{a}+\hat{b})$ is $\frac{1}{2}$
If
$\frac{\text{d}}{\text{dx}}\text{f}\text{(x)}=4\text{x}^3-\frac{3}{\text{x}^4}$such that $\text{f}(2)=0.$Then $\text{f}\text{(x)}$ is$A_1=\left\{(x, y): x \geq 0, y \geq 0,2 x+2 y-x^2-y^2>1>x+y\right\}$
$A_2=\left\{(x, y): x \geq 0, y \geq 0, x+y>1>x^2+y^2\right\}$
$A_3=\left\{(x, y): x \geq 0, y \geq 0, x+y>1>x^3+y^3\right\}$
Denote by $\left|A_1\right|,\left|A_2\right|$ and $\left|A_3\right|$ the areas of the regions $A_1, A_2$ and $A_3$ respectively. Then,