The indefinite integral of , denoted , is defined to be the antiderivative of. In other words, the derivative of is.
Since the derivative of a constant is 0, indefinite integrals are defined only up to an arbitrary constant. For example,, since the derivative of is. The definite integral of from to , denoted , is defined to be the signed area between and the axis, from to.
Both types of integrals are tied together by the fundamental theorem of calculus. This states that if is continuous on and is its continuous indefinite integral, then. This means. Conic Sections Transformation. Matrices Vectors. Chemical Reactions Chemical Properties. Integral Calculator Integrate functions step-by-step. Get step-by-step solutions from expert tutors as fast as minutes.
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