5/20 - Intro to Calculus - Check in

Solve the following differential equations:
 $\frac{\text{d}y}{\text{d}x}=\frac{1}{\cos y}$  

•  $\sin y=1+C$  

•  $\sin y=x+C$  

•  $-\sin y=\frac{x^2}{2}+C$  

•  $\sin y=0+C$  

Solve the following differential equations:
 $\frac{\text{d}y}{\text{d}x}=\frac{x}{y}$  

•  $\ln y=\frac{x^2}{2}+C$  

•  $y=\frac{x^2}{2}+C$  

•  $x^2=y^2+C$  

•  $y^2=x^2+2C$  

∫(4 - 18x)dx

• F(x) = -18
• F(x) = 4x - 9x²
• F(x) = 4x - 9x² + C
• F(x) = (4 - 18x)² /2 + C

 $\int e^xdx\ is\ equal\ to$  

•  $\frac{e^x}{x}+c$  

•  $e^x+c$  

•  $e^x$  

•  $\frac{e^x}{\ln\left(e\right)}$  

Identify the u and the du.

• u = 3x², du = -6x dx

• u = x³ + 1, du = 3x² dx

• $u=\sqrt{x^{3^{ }}+1}$ , $du=\frac{3x^2}{2\sqrt{x^3+1}}$

• $u=\sqrt{x^3+1}$ , $du\ =\ 3x^2dx$