<span>Our Sun will slowly get hotter as more and more Helium accumulates in the Sun's core. In ~1 billion years, liquid water will no longer be possible on Earth's surface, and the oceans will completely boil away, resulting in a Venus-like planet. Only thermophyllic bacteria may be able to survive, perhaps at the poles. In ~4-5billion years, our Sun will have converted ~10% of its Hydrogen to Helium, and thus become so hot that Helium to Carbon fusion will begin in earnest, causing the "Helium flash" which will convert our Sun into a red giant, and swallow and vaporize all of the rocky inner planets. It may even blow off a planetary nebula. (Contrary to what the others have said, our Sun will not 'run out' of Hydrogen.) </span>
Answer:
sec(4x) + C
Explanation:
original problem: ∫sec(4x)tan(x)dx
use integration by substitution (u-sub) by setting u = 4x
if u = 4x, then du/dx = 4 and du = 4dx (dx = du/4)
after substitution the integral is ∫sec(u)tan(u)(du/4)
move the 1/4 out of the integral by using the integral Constant rule to form 1/4∫sec(u)tan(u)du
the anti-derivative of sec(u)tan(u) is sec(u), memorize your trigonometric derivatives!!!!
after integration, we get sec(u)/4 + C , now plug u back into the equation
sec(4x) + C is the general solution
Indigenous bookkeeping is also known as a "single entry system"
Answer:
post - industrial
To me I think that's the best
