Definite Integral Properties

 $\int_{-a}^af\left(x\right)dx=$  

•  $0,\ if\ f\left(-x\right)=f\left(x\right)$  

•  $2\int_0^af\left(x\right),\ if\ f\left(-x\right)=f\left(x\right)$  

•  $2\int_0^af\left(x\right),\ if\ f\left(-x\right)=-f\left(x\right)$  

• none of these

 $\int_0^{2a}f\left(x\right)dx=$  

•  $2\int_0^af\left(x\right)dx,\ if\ f\left(2a-x\right)=f\left(x\right)$  

•  $2\int_0^af\left(x\right)dx,\ if\ f\left(2a-x\right)=-f\left(x\right)$  

•  $2\int_0^af\left(x\right)dx,\ if\ f\left(-x\right)=f\left(x\right)$  

•  $2\int_0^af\left(x\right)dx,\ if\ f\left(a-x\right)=f\left(x\right)$  

 $\int_0^af\left(x\right)dx=$  

•  $\int_0^af\left(a+x\right)dx$  

•  $\int_0^af\left(a-x\right)dx$  

•  $0$  

•  $2\int_0^af\left(x\right)dx$  

 $\int_{-3}^3\left|x+1\right|dx=$  

• 10

• 0

• 8

• none of these

 $\int_0^{\frac{\pi}{2}}\left(\frac{\sin x}{\sin x+\cos x}\right)dx=$  

•  $\frac{\pi}{2}$  

•  $\frac{\pi}{4}$  

• 0

•  $\pi$  

 $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\sin^9x\right)dx$  

•  $2\int_0^{\frac{\pi}{2}}\sin^9x\ dx$  

•  $\frac{\pi}{2}$  

• none of these

• 0

 $\int_0^a\left(\frac{\sqrt{x}}{\sqrt{x}+\sqrt{a-x}}\right)dx$  

•  $0$  

•  $\frac{a}{2}$  

•  $a\sqrt{2}$  

•  $2a$