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Riemann Sum and Definite Intergrals

Authored by Thomas Soucar

Mathematics

11th - 12th Grade

Used 9+ times

Riemann Sum and Definite Intergrals
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5 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Media Image

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

∫03 x2+3 dx\int_0^3\ x^2+3\ dx

∫13 x2+3 dx\int_1^3\ x^2+3\ dx

∫31 x2+3 dx\int_3^1\ x^2+3\ dx

∫13x2 +3 dy\int_1^3x^{2\ }+3\ dy

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which definite integral represents the area of the region enclosed by    y=9−x2y=\sqrt{9-x^2}  and the x-axis.

 ∫03 9−x2dx\int_0^3\ \sqrt{9-x^2}dx  

 ∫33 9−x2dx\int_3^3\ \sqrt{9-x^2}dx  

 ∫−33 9−x2dx\int_{-3}^3\ \sqrt{9-x^2}dx  

 ∫3−3 9−x2dx\int_3^{-3}\ \sqrt{9-x^2}dx  

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If  ∫25 f(x)dx=5 and  ∫45 f(x)dx=π, find ∫55 f(x)dx.\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.  

 −π-\pi  

 00  

 −0-0  

 π\pi  

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 If∫25 f(x)dx=5 and  ∫45 f(x)dx=π, find ∫54 f(x)dx.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.  

 00  

 −1-1  

 −π-\pi  

 π\pi  

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 ∫25 f(x)dx=5 and  ∫45 f(x)dx=π, find ∫24 f(x)dx.\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

 π−5\pi-5  

 22  

 5−π5-\pi  

 −(5−π)-\left(5-\pi\right)  

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