Calculus Final Exam

For the following equation, approximate the area under the curve over the given interval using 4 right endpoints.

Evaluate the indefinite integral.

 $\int_{ }^{ }\left(2x+2x^{-3}-6x^{-4}\right)dx$  

•  $x-x^{-3}+2x^4+C$  

•  $-2x+C$  

•  $x^2-x^{-2}+2x^{-3}+C$  

•  $2x^2+2x^{-2}-6x^{-3}+C$  

∫ 2x cos( x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + C

_{Evaluate the integral}

• 30/3
• 31/3
• 29/3
• 32/3

The graph of f consists of line segments and a semcircle, as shown. Evaluate the function by using geometric formulas, on interval [-5, 9]

On what interval(s) is the function y=x³ + 6x²

concave down?

• (-∞,-4)

• (-∞,-2)

• (-2,∞)

• (0,∞)

Approximate the area under $f\left(x\right)=\frac{x^2}{2}-x+1$   on [-3,1] using n =4 trapezoids. 

• 13.333

• 13

• 14

• 12.5

What is the limit?

• Infinity
• 20
• DNE
• 12

• 0

• 2

• 3

• 4

• Does not exist
• 6
• 4
• 3