What is the difference between definite and indefinite integrals?
Definite integrals produces a numerical answer. It is asking the question: what is the area under the curve f(x) between x=a and x=b.
Indefinite integrals produces a function. It is asking the question: what function F(x), when differentiated, gives f(x). The answer is a function of x + c (where c is an arbitrary constant)
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curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.
What does differentiation actually do?
The line L1 has vector equation, L1 = ( 6, 1 ,-1 ) + λ ( 2, 1, 0). The line L2 passes through the points (2, 3, −1) and (4, −1, 1). i) find vector equation of L2 ii)show L2 and L1 are perpendicular.