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Integrals in Summation Notation

Authored by Dan Schwanekamp

Mathematics

11th Grade - University

Used 94+ times

Integrals in Summation Notation
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13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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Which of the limits is equivalent to the following definite integral?

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2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 ∫25(x3+3)dx\int_2^5\left(x^3+3\right)dx  as limit of a sum is equivalent to

 lim⁡n→∞∑i=1n[(2+3in)3+3]1n\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{1}{n}  

 lim⁡n→∞∑i=1n[(2+3in)3+3]3in\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3i}{n}  

 lim⁡n→∞∑i=1n[(3in)3+3]3n\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{3i}{n}\right)^3+3\right]\frac{3}{n}  

 lim⁡n→∞∑i=1n[(2+3in)3+3]3n\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\frac{3}{n}  

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 ∫0πcos⁡xdx \int_0^{\pi}\cos xdx\   as limit of a sum is equivalent to

 lim⁡n→∞∑i=1n[cos⁡(πin)]in\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\frac{i}{n}  

 lim⁡n→∞∑i=1n[cos⁡(in)]in\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\frac{i}{n}  

 lim⁡n→∞∑i=1n[cos⁡(πin)]πn\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\frac{\pi}{n}  

 lim⁡n→∞∑i=1n[cos⁡(in)]πn\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\frac{\pi}{n}  

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 lim⁡n→∞∑i=1n[(5in)2+5in+1]5n\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{5i}{n}\right)^2+\frac{5i}{n}+1\right]\frac{5}{n}  in integral notation would be 

 ∫05(x2+x+1)dx\int_0^5\left(x^2+x+1\right)dx  

 ∫56(x2+x+1)dx\int_5^6\left(x^2+x+1\right)dx  

 ∫01((5x)2+5x+1)dx\int_0^1\left(\left(5x\right)^2+5x+1\right)dx  

 ∫010(x22+x2+1)dx\int_0^{10}\left(\frac{x^2}{2}+\frac{x}{2}+1\right)dx  

5.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

 lim⁡n→∞∑i=1n[2+3+4in]4n\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[2+\sqrt{3+\frac{4i}{n}}\right]\frac{4}{n}  in integral notation would be 

 ∫37(2+x)dx\int_3^7\left(2+\sqrt{x}\right)dx  

 ∫04(2+x)dx\int_0^4\left(2+\sqrt{x}\right)dx  

 ∫37(2x+x)dx\int_3^7\left(2x+\sqrt{x}\right)dx  

 ∫37(2+3+x)dx\int_3^7\left(2+\sqrt{3+x}\right)dx  

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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Which of the definite integrals is equivalent to the following limit?

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7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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Which of the limits is equivalent to the following definite integral?

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