Indefinite and definite integrals

Divide the interval  $\left[-1,2\right]$  into 4 subintervals of equal lengths and let x* be the midpoint of the third subinterval. Find x*

• 0.5

• 0.75

• 0.875

• 0.125

Which of the following is NOT true?

• Riemann sum can be positive or negative value

• Riemann sum is named after the German mathematician

• The total area of rectangles under the graph must overestimate the definite integral

• Riemann sum equals the definite integral when the length of each subinterval approaches 0

Find the AREA of the shaded region

• 0.2343

• 0.75

• - 0.5156

• 1.2656

 $\int_{ }^{ }\cos\left(2\cdot x\right)-\sqrt{x}\ \ dx$  =

•  $\frac{1}{2}\sin\left(2x\right)-\frac{2}{3}x^{\frac{3}{2}}+C$  

•  $-\sin\left(2x\right)+\frac{2}{3}x^{\frac{3}{2}}+C$  

•  $\sin\left(2x\right)+x+C$  

•  $\frac{1}{2}\cos\left(2\cdot x\right)\sin\left(2x\right)+\frac{2}{3}x^{\frac{3}{2}}+C$  

Which of the following is TRUE ?

• Antiderivative is the function that you get when you differentiate another function

• Antiderivative of f(x) = 2 is 0

• The Fundamental Theorem of Calculus part 2 gives us a way to evaluate the definite integral

• The process of finding derivative is called integration