1a. Simple integration
x²dx
x²dy
dx
3dy
sin 3x dx
cos x/4 dx


(tan² x+1)dx
3sin⁴x cos dx
sec²x tanxdx
(4x²-3x+2)dx
csc 5x cot 5x dx

1(b) definite intergrals

2. Sigma notation

3. Find area of region bounded by given curves
y = x² -x and y=0
y = cos x, y = 0, between x = 0 & x = p / 2
y = x³ - 3x², x - y = - 3

4 . 2nd Fundamental theorm of Calculus

If , find F ' (x)

5. Find average value of f(x) = sin x over integral [0, p ]

6. Log and exponental review

Solve exponential equations

3^{2x + 3} = 8^{3x - 4}

Solve logarithmic equations
log (x² - 4) - log (x - 4) = 2

Graph of log and exponential equations

y = log₃ x , y = log _1/2 x

y = 5^x , y = (1/2)^x

7. Differentiate y = ln f(x)

y = ln(x² + 5x -9)

y = ln (sin²x)
y = log_af(x)

8. Intergrate du/u