Answer:
<u>Given equations</u>: y = 3x² + x - 6; y = x - 4
So, Plug the value of value of y in other equation
- 3x² + x - 6 = x - 4
- 3x² + x - x - 6 + 4 = 0
- 3x² - 2 = 0
- 3x² = 2
- x² = 2/3
- x = √2/3
Because its two 3s in the median i thought it give it a higher chance.
We are asked in the problem to evaluate the integral of <span>(cosec^2 x-2005)÷cos^2005 x dx. The function is an example of a complex function with a degree that is greater than one and that uses special rules to integrate the function via the trigonometric functions. For example, we integrate
2005/cos^2005x dx which is equal to 2005 sec^2005 x since sec is the inverse of cos. The integral of this function when n >3 is equal to I=</span><span>∫<span>sec(n−2)</span>xdx+∫tanx<span>sec(n−3)</span>x(secxtanx)dx
Then,
</span><span>∫tanx<span>sec(<span>n−3)</span></span>x(secxtanx)dx=<span><span>tanx<span>sec(<span>n−2)</span></span>x/(</span><span>n−2)</span></span>−<span>1/(<span>n−2)I
we can then integrate the function by substituting n by 3.
On the first term csc^2 2005x / cos^2005 x we can use the trigonometric identity csc^2 x = 1 + cot^2 x to simplify the terms</span></span></span>
31/18 is the answer.
To solve, find the common denominator. In this case, I used 54. You need to multiply each fraction to get 54 on the denominator of both.
Try using photomath it works very well
