Technique 1 - Direct Integration: The most straightforward approach. Identify upper and lower curves, find intersection points, and integrate (upper - lower) dx. Works for polynomials, simple trigonometric, exponential, and logarithmic functions.

Technique 2 - Substitution: When the integrand contains composite functions. For area under y = sqrt($a^2$ - $x^2$), substitute x = a*sin(theta). For y = sqrt(ax + b), substitute u = ax + b. The substitution changes both the integrand and the limits.

Technique 3 - Integration by Parts: Needed for area under y = x*$e^x$, y = xln(x), y = xsin(x), etc. Also for inverse trigonometric functions: integral of sin^(-1)(x) dx uses u = sin^(-1)(x), dv = dx.

Technique 4 - Symmetry Reduction: Before integrating, check for even/odd symmetry. Even: double the half. Odd: signed integral is zero. Periodic: count the number of periods and multiply by one period's area.

Technique 5 - Complement Method: Instead of computing the desired area directly, compute the complement within a known region. Example: area above a line inside a circle = sector area - triangle area. Also: area to the left of a curve = rectangle area - area below the curve.

Technique 6 - Horizontal vs Vertical Strips: Choose the orientation that minimizes the number of integral pieces. Parabolas $y^2$ = 4ax are best handled with horizontal strips. Circles and ellipses can go either way.

Technique 7 - Parametric Integration: When curves are given parametrically, use A = integral of y(t)*x'(t) dt directly rather than eliminating the parameter.

Technique 8 - Standard Result Application: When the problem reduces to a known configuration (e.g., parabola + line), apply the memorized formula directly. This is the fastest method for JEE.