Definite Integrals and Special Functions — Study Resources & PYQs
Definite integrals with important properties, differentiation under the integral sign, Gamma, Beta and error functions with simple problems.
- Estimated study time: 105 minutes
Study resources
- GeeksforGeeks – Definite Integral (Article) — Definition, the key properties of definite integrals and how to evaluate them, with examples.
- NPTEL (IIT Kanpur) – Mathematics II (Article) — Free IIT video+notes course covering definite integration, multiple integrals and related calculus rigorously.
- Physics LibreTexts – Differentiating Under the Integral Sign (Article) — Friendly walkthrough of Leibniz's rule (a.k.a. Feynman's trick) with a clear method and solved examples.
- Educative – What is the Leibniz Integral Rule? (Article) — Short, exam-focused page giving the formula and a couple of quick solved problems.
- GeeksforGeeks – Gamma Function (Article) — Definition (Euler's integral of the second kind), recurrence relation Γ(n+1)=nΓ(n), and Γ(n)=(n-1)! with examples.
- GeeksforGeeks – Beta Function (Article) — Definition, the Beta–Gamma relation β(p,q)=Γ(p)Γ(q)/Γ(p+q), properties and trig-integral applications.
- TheEngineeringMaths – Beta & Gamma Functions (notes) (PDF) — Concise notes with several solved problems reducing definite integrals to Beta/Gamma form. Handy for quick revision.
- Math for Engineers – The Error Function Erf(x) (Article) — Definition of erf(x), its graph, odd-function property and link to the normal distribution, with the basic formula.
- Wikipedia – Error Function (Article) — Comprehensive reference: definition, series expansion, complementary error function erfc and key properties.
Taught in these subjects
- ENGINEERING MATHEMATICS-1 — BMAT11 · Government College of Engineering and Technology, Jammu