Calculus & Analytic Geometry (B.A / B.Sc.)
Chapter:04 (Definite Integrals, Improper Integrals)
In this chapter, we will study the following topics:
- definite integral
- lower sum
- refinement of P
- first division point of P
- definite integral
- f is integrable
- Riemann integral
- Reimann (a German mathematician)
- a finite number of points finite discontinuity
- the fundamental theorem of the integral calculus
- upper limit
- integrand
- lower limit
- the range of integration
- definite integral
- f is continuous on F
- first principle of integration
- mean value theorem of integral calculus
- geometrical significance of definite integral
- area under the graph of the sine function
- area bounded by the curve
- area above the given interval
- reduction formulae
- indefinite integrals
- improper integrals
- convergent integral
- improper integral of second kind
- integrals in which the lower limit of integration is not finite
- beta and gamma integrals
- taylor’s expansion
- stirling’s formula
- if curve is lemniscate
- proofs of some theorems of definite integrals
- proofs of some theorems on Beta and Gamma functions
- resulting series
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