4 sinx / cosx * cosx
4 tanx / cosx Trig identity tanx = sinx/cosx
Hey, I know this is kinda rare but I’m a Sophomore in High School taking four AP classes also (AP: Bio, Physics, Com. Sci., and World History)
It’s my first time having this work load, and it is pretty overwhelming at times.
For you, I’d say: do what benefits you the most. Always remember that time management is key. What ever you have time for is what you can do. You can talk to your counselor also. Especially, your teachers can help too. If you really do want to keep your classes, prioritize and do your best. I hope this helped a bit.
Good luck :-) Best Wishes.
Your voltmeter and your teacher are both right, but the water analogy of electricity can only go so far. One big drawback is that, unlike with water, there is no absolute voltage. .... Wherever you put the black lead is defined as "0V". .... flowing (i.e. the circuit is broken) you will not get this change in voltage.
(1) The integral is straightforward; <em>x</em> ranges between two constants, and <em>y</em> ranges between two functions of <em>x</em> that don't intersect.

(2) First find where the two curves intersect:
<em>y</em> ² - 4 = -3<em>y</em>
<em>y</em> ² + 3<em>y</em> - 4 = 0
(<em>y</em> + 4) (<em>y</em> - 1) = 0
<em>y</em> = -4, <em>y</em> = 1 → <em>x</em> = 12, <em>x</em> = -3
That is, they intersect at the points (-3, 1) and (12, -4). Since <em>x</em> ranges between two explicit functions of <em>y</em>, you can capture the area with one integral if you integrate with respect to <em>x</em> first:

(3) No special tricks here, <em>x</em> is again bounded between two constants and <em>y</em> between two explicit functions of <em>x</em>.
