Month: July 2015

Find the area of the region in the first quadrant bounded by the line y = 2x, the line x = 3, the curve y = , and the x…

Find the area of the region enclosed by the curve y = 5sin x and y = sin (5x) , 0 ≤ x ≤ π.   Solution:-   The area…

Find the area of the region enclosed by the curves y2 – 3x = 4 and x – y = 2.   Solution:-   The area of the region enclosed…

Find the area bounded by the graphs of the indicated equations. y = x4 – 4×2 + 1 y = x2 – 3   Solution:-   The are bounded by…

Solve the initial value problem .   = 20t(5t2-3)3 , s(1) = 12   Solution:-   The solution is s  =  (5t2-3)4+4.          

Solve the initial value problem. = 36(9t2-7)3, s(1) = 9   Solution:-   To solve this initial value problem for s as a function of t, note that =f(t) →…

Evaluate the indefinite integral by using the given substitution to reduce the integral to standard from. ∫14csc2(7x)cot(7x)dx, a. u =  cot(7x), b. u = csc(7x)   Solution:-   Using u…

Evaluate the indefinite integral by using the given substitution to reduce the integral to standard from. ∫ 6sec2(3x)tan (3x)dx, a. u = tan(3x) b.  u = sec(3x)   Solution:-  …

Find the total area of the region between the x-axis and the graph of y = – x2 – 3x , -5 ≤ x ≤ 4.   Solution:-   The…

Use a definite integral to find the area of the region between the curve y = 3x and the x-axis on the interval [0,b]   Solution:-   The area of…