Using Definite Integral Properties

[pdeepakm]

Been watching your videos for a year now. Just dropping by to say, "You're awesome!"

[tambuwalmathsclass]

Keep doing the good work. We wont get tired of watching

[shivi]

Thanks for teaching so beautifully...🌻💛

[hanshans]

Eddie, you're such a great teacher, so good at communicating tricky concepts - thank you so much!

[JohnSmith-rftx]

In part (e) it was really quite naughty of the textbook authors to use angle measurements in degrees for the boundaries of integration. The rules for differentiation or integration of trigonometric functions only work when discussing angles in radians. Thank goodness the structure of the question meant that an actual evaluation wasn't called for.

[josephcoon]

The symmetry of a function is determined by the extreme cases of x and -x. In a polynomial, the term with the highest power will have the ultimate effect on the function when x equals infinity or negative infinity. The only distinction between infinity and negative infinity is the sign. Any number raised to any power will keep the same sign. Symmetry is determined by what the left hand of the graph (-x) does compares to the right hand of the graph (x).

Positive numbers can be viewed as +1 times the absolute value of that number. Negative numbers can be viewed as -1 times the absolute value of that number. Taking a number to a power can then be broken down into the absolute value of a number to that power times, either +1 or -1 taken to the same power. Since comparing the left and right if the graph comes down to comparing -1 times infinity to +1 times infinity, you can disregard infinity and address -1 and +1.

-1 taken to any positive power will result in +1 just as +1 taken to that same power also results in +1. If negative infinity and positive infinity both result in the same sign, the function is bilaterally symmetric (mirror).

Now, -1 taken to an odd power results in -1 while +1 taken to the same power results in +1. This means that -infinity does the exact opposite of +infinity resulting in rotational symmetry.

Simply put: the results of -infinity and +infinity in a polynomial is determined by the largest magnitude term. If that magnitude is odd, the function has rotational symmetry. If that magnitude is even, the function has bilateral symmetry.

[nahidkausarsyed]

Kindly, which book to use for Cambridge o level maths.

[markitsche]

Thank you, Sir. This is a tricky exam.

[mertfreeman]

my English is not very good to understand you, but I watch you with pleasure. Good videos!

[TheKennethMichael]

I’ve asked this question before, but I cannot remember now. What software do you use Eddie?

[duddekeshavakumar]

Sir, plz tell me which app u r using for teaching

[mushtaqhussain]

Sir the limits of integral must be in the domain of function to be integreted?

[onyxtautuhi]

9:53 looks like a small sawtooth wave. LOL

[yusufat]

part (a) is a semicircle, and I ended up using simple geometry yay

[fanylobo]

These integrals are very easy sir . Sir once in a lifetime try attempting INDIA'S JEE Advance paper I hope it will blow your mind

[沈博智-xy]

11:28 haha. so tempting to see 1+x^2 and use trig sub.