Riemann Sum and Definite Intergrals

Which of the following definite integrals represent the area of the shaded region? (Scaled by ones)

• $\int_0^3\ x^2+3\ dx$

• $\int_1^3\ x^2+3\ dx$

• $\int_3^1\ x^2+3\ dx$

• $\int_1^3x^{2\ }+3\ dy$

Which definite integral represents the area of the region enclosed by    $y=\sqrt{9-x^2}$  and the x-axis.

•  $\int_0^3\ \sqrt{9-x^2}dx$  

•  $\int_3^3\ \sqrt{9-x^2}dx$  

•  $\int_{-3}^3\ \sqrt{9-x^2}dx$  

•  $\int_3^{-3}\ \sqrt{9-x^2}dx$  

If  $\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_5^5\ f\left(x\right)dx.$  

•  $-\pi$  

•  $0$  

•  $-0$  

•  $\pi$  

 $If\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_5^4\ f\left(x\right)dx.$  

•  $0$  

•  $-1$  

•  $-\pi$  

•  $\pi$  

 $\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_2^4\ f\left(x\right)dx.$  If

•  $\pi-5$  

•  $2$  

•  $5-\pi$  

•  $-\left(5-\pi\right)$