Equation of the tangent line
i) Fundamental Theorem of calculus. If f(x) is continuous on [a, b] and
i) Slope point form:
4) Calculation:The slope of tangent to the curve at x is given by derivative at x.
By using Fundamental Theorem of Calculus,
Given that, x=π,
Substitute value of x in F’(x)
Therefore, slope of tangent line at x=π is
-1π At x=π
Fx=∫πxcostt dt= ∫ππcosxx dx=0 since upper and lower limits of integral are same.
Use point slope form to find equation of tangent line,
Now, m=-1π and x1=π ,y1=0
Substituting the value,
Applying distributive property,
This is the equation of tangent line to the curve, y=Fx at the point π,0.
Therefore, the equation of tangent line is