Sample Problems

calc2

Logger Problem

Recently, I was helping a UMich student prepare for a test on series and sequences. He brought along a practice exam for us to go through that included this...

Take the Derivative Instead

Integration by parts allows us to use a strategy I like to call “take the derivative instead” for certain integrals, such as these:

Inverse Trig Triangle Method

Here’s something that becomes important for certain integrals in calc 2. Let’s simplify this expression fully, removing all trig:

Inverse Tangent U-Sub

I see a lot of students struggling to see when an integral is related to inverse trig. Let’s take a look at the inverse tangent in this post. If an integra...

Partial Fractions Integral 1

One of my students one day asked me to come up with some practice problems for partial fractions integrals. Soon after that, while camping, I challenged mys...

Kite Area Optimization

Let’s say we have 4 metal rods, 2 of length a and 2 of length b. We want to arrange these metal rods into a kite. How long should the diagonals of the kite...

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integral

Take the Derivative Instead

Integration by parts allows us to use a strategy I like to call “take the derivative instead” for certain integrals, such as these:

Inverse Tangent U-Sub

I see a lot of students struggling to see when an integral is related to inverse trig. Let’s take a look at the inverse tangent in this post. If an integra...

Partial Fractions Integral 1

One of my students one day asked me to come up with some practice problems for partial fractions integrals. Soon after that, while camping, I challenged mys...

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calc1

Inverse Tangent U-Sub

I see a lot of students struggling to see when an integral is related to inverse trig. Let’s take a look at the inverse tangent in this post. If an integra...

Kite Area Optimization

Let’s say we have 4 metal rods, 2 of length a and 2 of length b. We want to arrange these metal rods into a kite. How long should the diagonals of the kite...

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optimization

Kite Area Optimization

Let’s say we have 4 metal rods, 2 of length a and 2 of length b. We want to arrange these metal rods into a kite. How long should the diagonals of the kite...

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partialfractions

Partial Fractions Integral 1

One of my students one day asked me to come up with some practice problems for partial fractions integrals. Soon after that, while camping, I challenged mys...

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usub

Inverse Tangent U-Sub

I see a lot of students struggling to see when an integral is related to inverse trig. Let’s take a look at the inverse tangent in this post. If an integra...

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inversetrig

Inverse Tangent U-Sub

I see a lot of students struggling to see when an integral is related to inverse trig. Let’s take a look at the inverse tangent in this post. If an integra...

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log

Inverse Tangent U-Sub

I see a lot of students struggling to see when an integral is related to inverse trig. Let’s take a look at the inverse tangent in this post. If an integra...

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naturallog

Inverse Tangent U-Sub

I see a lot of students struggling to see when an integral is related to inverse trig. Let’s take a look at the inverse tangent in this post. If an integra...

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trig

Inverse Trig Triangle Method

Here’s something that becomes important for certain integrals in calc 2. Let’s simplify this expression fully, removing all trig:

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IBP

Take the Derivative Instead

Integration by parts allows us to use a strategy I like to call “take the derivative instead” for certain integrals, such as these:

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series

Logger Problem

Recently, I was helping a UMich student prepare for a test on series and sequences. He brought along a practice exam for us to go through that included this...

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sequence

Logger Problem

Recently, I was helping a UMich student prepare for a test on series and sequences. He brought along a practice exam for us to go through that included this...

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limit

Logger Problem

Recently, I was helping a UMich student prepare for a test on series and sequences. He brought along a practice exam for us to go through that included this...

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