Definite Integrals

Concept Quizzes

Definite Integrals Warmup
Basic Properties of Integrals
Riemann Sums
Fundamental Theorem of Calculus

Challenge Quizzes

Definite Integrals: Level 2 Challenges
Definite Integrals: Level 3 Challenges

Definite Integrals Warmup

The graph of the function $y = f(x)$ is shown above. What is the value of $\int_0^6 f(x) dx?$

12 15 18 30

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by Brilliant Staff

Steve knows that if he uses right-hand endpoints with 2 subintervals to find a Riemann sum approximation of $\int_0^8 x dx,$ his approximation will be the sum of the areas of the 2 rectangles shown. Assuming all his work is correct, what will his approximation be?

16 18 48 64

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by Brilliant Staff

Morgan and Pat use right-hand endpoints to find Riemann sum approximations of $\int_0^8 x dx.$

If Morgan uses 2 subintervals, and Pat uses 4 subintervals, whose approximation is closer to the true value of the integral?

Morgan's (2 subintervals) Pat's (4 subintervals)

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by Brilliant Staff

Ferb knows that $\int_0^8 x dx = 32,$ and is interested in how close a right-hand Reimann sum approximation to the integral can be.

Based on his work so far, if Ferb uses 32 subintervals, what will his approximation be?

Number of subintervals	Approximation	Error
1	64	32
2	48	16
4	40	8
8	36	4
16	34	2
32	??

32 32.125 33 34

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by Brilliant Staff

$A = \int_{1}^{2} x dx, \,\,\,\, B = \int_{1}^{2} x^2 dx$

Which of the following is true of $A$ and $B?$

A<B

B<A

A = B

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by Brilliant Staff