#### To determine

**To find:**

Equation of the tangent line

#### Answer

y=-xπ+1

#### Explanation

**1) Concept:**

i) Fundamental Theorem of calculus. If f(x) is continuous on [a, b] and

gx=∫axf(t) dt

then g'x=f(x)

**2) Formula:**

i) Slope point form:

y-y1=m ·(x-x1)

**3) Given:**

Fx=∫πxcostt dt

**4) Calculation:**The slope of tangent to the curve at x is given by derivative at x.

Here

Fx=∫πxcostt dt

By using Fundamental Theorem of Calculus,

F’x= cosxx

Given that, x=π,

Substitute value of x in F’(x)

F’(π)=cosππ

Since, cosπ=-1

F’π=-1π

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.

Therefore, Fπ=0

Use point slope form to find equation of tangent line,

y-y1=m ·(x-x1)

Now, m=-1π and x1=π ,y1=0

Substituting the value,

y-0=-1π ·(x-π)

y=-1π ·(x-π)

Applying distributive property,

y=-xπ+1

This is the equation of tangent line to the curve, y=Fx at the point π,0.

**Conclusion:**

Therefore, the equation of tangent line is

y=-xπ+1