Explanation Please

[balmy sundial]

I need an explanation of the process of how this integration in finding area bounded by the equation y = x^2 - 4 and y = x^2+7x comes to 243/8 and/or -243/8 as an answer. Like am I suppose to multiply the equation? am I suppose to work them separately? I tried everything I could and still not get the answer.

[edgy escarp]

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[queen saffron]

A property of definite Integrals is that integrals of two functions can be added or subtracted (like in algebra) provided limits are equal, so you can subtract the two functions here and then evaluate them

Or evaluating separately doesn't make any difference

[balmy sundial]

My problem is when I tried seperately or multiply them into one, i do not get 243/8 (or in -) as an answer but some other answers e.g. 99/8

[sage axle]

what do u mean?

[balmy sundial]

if i multiply the equations into one, and integrate, it does not become 243/8 (or in -), even integrating them separately wouldnt give 243/8, but when i insert the integral equation onto the calculator, it shows me 243/8 but i do not know if i am doing something wrong in the working or inserting something wrong in the calculator

because i was given some work/question where i have to multiply the equations into one and integrate it and some w/o multiplying

cause i am trying to find the bounded area

[sage axle]

u dont multiply the integrals

if ur not sure which curve covers larger area, subtract either from the other and taking modulus of the value

like the other person said, u can add or subtract definite integrals provided they have the same limits

[balmy sundial]

if i cant multiply, then why in my example which is written on paper, 3 as upperlimit, 1 as lower limit with its equation x dx - x^2 - x - 3 dx becomes x-(x^2-x-3) dx and then -x^2 + 2x + 3 dx?

r = integral curve above - curve below no?

[sage axle]

thats not multiplying

thats subtracting the two curves

u distribute the negative sign within the quadratic curve to get -x^2+x+3

which added to x is -x^2+2x+3

[sage axle]

yeah or alternatively u can subtract any of the curves and take the modulus so u get rid of the negative area

[balmy sundial]

I tried doing it again and i still dont end up with 243/8..

Nevermind

I found my mistake

Thanks for trying to help x))

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