Integration as the limit of a sum (AQA A-Level Mathematics): Quizzes

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Integration as the limit of a sum
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What does integration as the limit of a sum define the integral as?

The limit of a sum of rectangle areas

What is the width Δx\Delta x of each subinterval when [a,b][a, b] is divided into nn parts?

Δx=b−an\Delta x = \frac{b - a}{n}

What happens to the Riemann sum as nn increases?

Becomes better approximation

What is the general form of a Riemann sum?

Sn=∑i=1nf(xi∗)ΔxS_n = \sum_{i=1}^n f(x_i^*) \Delta x

Where is the sample point xi∗x_i^* located in a Left Riemann Sum?

Left endpoint

Where is the sample point xi∗x_i^* located in a Right Riemann Sum?

Right endpoint

Where is the sample point in a Midpoint Riemann Sum?

Midpoint of subinterval

What shapes does the Trapezoidal Rule use instead of rectangles?

Trapezoids

How is the definite integral ∫abf(x)dx\int_a^b f(x) dx defined using limits?

lim⁡n→∞∑i=1nf(xi∗)Δx\lim_{n \to \infty} \sum_{i=1}^n f(x_i^*) \Delta x

What is ∫01x2dx\int_0^1 x^2 dx using integration as limit of sum?

13\frac{1}{3}

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