Integral calc 1

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Last updated 10:37 PM on 7/16/26
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37 Terms

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Integral

Integration is the reverse process of differentiation

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Power Rule

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Integrand

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Integral

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Indefinite Integral / Antiderivative / Primitive Integral

Integral with no restrictions imposed in its independent variables

<p>Integral with no restrictions imposed in its independent variables</p>
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Definite Integral

Integral that is defined by the limit values a and b of the independent variable

<p>Integral that is defined by the limit values a and b of the independent variable</p>
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logarithm, exponent or trigonometric function

In u-substitution, u can be equal to mostly ___

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Integration by parts

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L-logarithm
I-inverse

A-alegebraic

T-trigo

E-exponential

Priority in IBP

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  1. Assign x=1.1

  2. CALC the function using the x value

  3. STO result to A

  4. Compare A to the derivative of the choices

d/dx(choice) @ x=1.1 / A

  1. Correct answer should be equal to 1

Calcu tech for integral

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  1. Apply linearity (if necessary) ex. ∫(x+y)dxdy=∫xdxdy+∫ydxdy

  2. Pair the limits to its corresponding differential coefficient

  3. Get the innermost pair and everything in between

Steps in computing for Multiple Integrals

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Riemann Sum

method for approximating the area under a curve by dividing the area into many small rectangles and adding up their areas

<p>method for <strong>approximating the area under a curve</strong> by dividing the area into many small rectangles and adding up their areas</p>
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change in x formula in riemann sum

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Left reiemann sum

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Right reiemann sum

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Midpoint reimann sum

<p></p>
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Sample point xi of left riemann sum

xi-1

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Sample point xi of right riemann sum

xi

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Sample point xi of midpoint riemann sum

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Vertical strip

Area by integration

<p>Area by integration</p>
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Horizontal strip

Area by integration

<p>Area by integration </p>
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<p></p>

Area by integration in Polar Coordinates

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<p>Special Polar Graphs of Rose Curve</p>

Special Polar Graphs of Rose Curve

the limit to be used is their corresponding period

<p>the limit to be used is their corresponding period</p>
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Special Polar Graphs of Rose Curves

the limit to be used is their corresponding period

<p>the limit to be used is their corresponding period</p>
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Special Polar Graphs of Limacon with inner loop

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Special Polar Graphs of Limacon with cardioid (heart-shaped)

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Special Polar Graphs of Limacon with Dimpled limacon

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Special Polar Graphs of Limacon with convex limacon

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<p></p>

Formula to be used in the Special polar graphs up or down

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Formula to be used in the Special polar graphs left or right

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<p></p>

Special Polar Graphs of Circles

<p>Special Polar Graphs of Circles</p>
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<p></p>

Special Polar Graphs of Circles

<p>Special Polar Graphs of Circles</p>
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<p></p>

Special Polar Graphs of Lemniscate

<p>Special Polar Graphs of Lemniscate</p>
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Special Polar Graphs of Lemniscate

<p>Special Polar Graphs of Lemniscate</p>
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