Integrals, derivatives and sums

5.1Find a definite integral#

Press ∫ to open the integral template. Type the function using ALPHAx) for x, press ▶ to move to the lower limit, type it, press ▶ again and type the upper limit. The integral is calculated numerically and shown exactly when it can be.

Example 5.1

The area under x² from 0 to 1

1. Integral, x, squared.

   ∫ALPHAx)x²

2. Right to the lower limit 0, right to the upper limit 1, equals.

   ▶0▶1=

Example 5.2

The area under 2x from 0 to 3

1. Integral, 2x.

   ∫2ALPHAx)

2. Limits 0 and 3.

   ▶0▶3=

$$\int_0^1 x^2\,dx=\frac13$$

5.2Find the slope at a point#

SHIFTd/dx∫ opens the derivative template: type the function, press ▶ and type the x value where you want the slope.

Example 5.3

Slope of x² at x = 3

1. SHIFT integral, x, squared.

   SHIFTd/dx∫ALPHAx)x²

2. Right, type 3, equals.

   ▶3=

$$\left.\frac{d}{dx}x^2\right|_{x=3}=2x\Big|_{x=3}=6$$

5.3Add up a series with Σ#

SHIFTΣlog opens the summation template: the expression, the start value and the end value. Use ▶ to move between the boxes.

Example 5.4

Sum of x² from 1 to 5

1. SHIFT log□, x, squared.

   SHIFTΣlogALPHAx)x²

2. Start 1, end 5.

   ▶1▶5=

$$\sum_{x=1}^{5}x^2=1+4+9+16+25=55$$

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