The aggregate demand curve is downward sloping. It implies price levels are falling and the quantity of output will increase as well as the domestic income. The theories that can explain why the aggregate demand curve is downward sloping: the Pigou's wealth effect, the Keynes's interest-rate effect, and the and Mundell-Fleming's exchange-rate effect.

7 0

2 years ago

Integrate sec(4x)tan(4x)dx

emmainna [20.7K]

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

4 0

3 years ago