$I=\int {e^x*cos(3x)} \, dx =e^x*(k_1/cos(3x)+k_2*sin(3x) )\\\\Let's\ derivate:\\\\e^xcos(3x)=e^x(k1*cos(3x)+k_2*sin(3x))+e^x*(k_1*(-sin(3x))*3+k_2*cos(3x)*3)\\\\By\ identification:\\\\\left\{\begin{array}{ccc}k_1+3k_2&=&1\\-3k_1+k2&=&0\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}k_1&=&\dfrac{1}{10}\\k2&=&\dfrac{3}{10}\\\end{array}\right.\\\\\\\boxed{I=e^x(\dfrac{1}{10}*cos(3x)+\dfrac{3}{10}*sin(3x))}\\$

8 0

2 years ago

A dog is leashed to a point in the center of a large yard. If the leash is 18.8 feet long, what is the total area of the region

Orlov [11]

Answer:

1109.8 square feet

Step-by-step explanation:

In this case, assume the leash to be the radius of the circular yard.

Area

πr²
3.14 x (18.8)²
3.14 x 353.44
1109.8 square feet

5 0

3 years ago

Use the graph of the function y = 4x to answer the following questions.

Likurg_2 [28]

Answer: negative infinity to positive infinity.

Step-by-step explanation:

3 0

4 years ago