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JEE Main Mathematics

Integral Calculus

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A timed sectional mock on this unit

Integration by substitution, by parts and by partial fractions, the standard forms, definite integrals and their properties, and areas bounded by simple curves.

Key formula
∫abf(x) dx=∫abf(a+b−x) dx,∫u dv=uv−∫v du\int_{a}^{b} f(x)\,dx = \int_{a}^{b} f(a+b-x)\,dx, \quad \int u\,dv = uv - \int v\,du

What this unit covers

  • Integral as an anti-derivative

  • Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions

  • Integration by substitution, by parts and by partial fractions

  • Integration using trigonometric identities

  • Simple integrals of the type ∫dx/(x² + a²), ∫dx/√(x² ± a²), ∫dx/(a² − x²), ∫dx/√(a² − x²), ∫dx/(ax² + bx + c), ∫dx/√(ax² + bx + c), ∫(px + q)dx/(ax² + bx + c), ∫(px + q)dx/√(ax² + bx + c), ∫√(a² ± x²)dx and ∫√(x² − a²)dx

  • The fundamental theorem of calculus

  • Properties of definite integrals, evaluation of definite integrals

  • Areas of the regions bounded by simple curves in standard forms

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