Evaluate 3x e5x dx Find the area bounded by the x axis y

Evaluate 3/x - e5x dx Find the area bounded by the x - axis, y = x2 - 4x, x = 1, and x = 5. Find the area between the curves y = x2 - 6x and y = - x.

Solution

₁³ (3/x-e^5x) dx

= [3ln|x| - e^5x/5] ₁³

= 3(ln|3| - ln|1|) - (e¹⁵-e⁵)/5

= 3ln(3) - (e¹⁵-e⁵)/5