Math is a difficult subject. Some people get it right away, and others struggle.

A lot of people find calculus difficult, and I’m happy to help them get through it!

It’s no problem. Sometimes the work can be a little tricky, but if you ever need more help, just ask!

integral from 0 to 2 of (x+5)dx/sqrt(4-x^2)

Split into two integrals:

= integral from 0 to 2 of xdx/sqrt(4-x^2) + integral from 0 to 2 of 5dx/sqrt(4-x^2)

1st integral:

u = 4-x^2

du = -2xdx

xdx = -du/2

u(0) = 4

u(2) = 0

2nd integral:

a = 2

u = x —> du = dx (not substitution, just confirming the arcsin identity)

Rewrite:

integral from 4 to 0 of xdx/sqrt(4-x^2) + integral from 0 to 2 of 5dx/sqrt(4-x^2)

= integral from 4 to 0 of -du/2sqrt(u) + integral from 0 to 2 of 5dx/sqrt(4-x^2)

= -sqrt(u) from 4 to 0 + 5arcsin(x/2) from 0 to 2

= [-sqrt(0) + sqrt(4)] + [5arcsin(1) - 5arcsin(0)]

= 0 + 2 + 5pi/2 - 0

= **2 + 5pi/2**

http://baronsledjoys.tumblr.com/post/93067055294/crowdsourcing-for-calculus-help

This post explains everything!

baronsledjoys, I emailed you like you wanted! Ask if you need more help ok!

breakdown of a free response question from the calc 2013 exam for those who intend to take the exam in the future

im guessing you mean integrating it so here it goes:

dy/dx=e^x*y^2

get one side in terms of y and the other in terms of x

dy/y^2 = e^xdx

integrate both sides

-1/y = e^x + C

rearrange to get in terms of y

-y = e^(-x) + C

**y = -e^(-x) + C**

[this is all assuming that dy/dx=e^x*y^2 = (e^x)(y^2) and not e^(xy^2)]

Help?

**Variables:**

A grade = A = 1792

B grade = B = 1600

Economy blend = E

Superior blend = S

Profit = P = E+3S *(what you want to maximize)*

**Restrictions:**

A grade: (4/16)E + (8/16)S </= 1792

0.25E + .5S </= 1792

*(4 of the 16 ounces in 1 pound of E are from A; 8 of the 16 ounces in one pound of S are from A; the total amount of A cannot exceed 1792 ounces)*

B grade: (10/16)E + (2/16)S </= 1600

0.625E + 0.125S </= 1600

*(10 of the 16 ounces in E are from B; 2 of the 16 ounces in S are from B; the total amount of B cannot exceed 1600 ounces)*

E > 0

S > 0

**Solve with substitution**:

0.25E + .5S = 1792

.5S = 1792 – 0.25E

S = 3584 – 0.5E

0.625E + 0.125S = 1600

0.625E + (0.125)(3584 – 0.5E) = 1600

0.5625E + 448 = 1600

0.5625E = 1152

E = 2048 ounces —> 2048/16 = **128 packages of economy blend**

S = 3584 – (0.5)(2048) = 3584 – 1024 = 2560 ounces —> 2560/16 = **160 packages of superior blend**

it can give away **4 large prizes and 25 small prizes**

(4)(125) = 500

(25)(40) = 1000

500+1000 = 1500