Fundamental Theorem of Calculus

_{Evaluate the integral}

• 30/3
• 31/3
• 29/3
• 32/3

Tags

CCSS.HSA.APR.A.1

• 12/3
• 6.5
• 5.5
• 11/3

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Find the area under a curve defined by the equation 5x⁴+3x+7 between the x values 0 and 4.

• 1200
• 1/12
• 1134
• 1076

Tags

CCSS.HSA.APR.A.1

 $\int_1^5\left(-x^2+6x-10\right)dx$  

•  $\frac{28}{3}$  

•  $\frac{-28}{3}$  

• 28

•  $-\frac{7}{2}$  

Tags

CCSS.HSA.APR.A.1

 $\int_{-2}^2\left(5x^{\frac{1}{3}}\right)dx$  

• 0
  

• -3

•  $-\frac{3}{2}$  

• -1

Let  $F\left(x\right)=\int_0^xf\left(t\right)dt$  , where the graph of  $f\left(x\right)$  above consists of lines and a quartercircle. Determine  $F\left(3\right)$ . 

• A
• B
• C
• D

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Underestimate or overestimate?

• Overestimate
• Underestimate

What is the Fundamental Theorem of Calculus?

• ∫[f(x) dx] = f(a - b) (lower limit=a; upper limit=b)

• ∫[f(x) dx] = F(a - b) (lower limit=a; upper limit=b)

• ∫[f(x) dx] = F(b) - F(a) (lower limit=a; upper limit=b)

• ∫[f(x) dx] = F(a) - F(b) (lower limit=a; upper limit=b)