Dr. J's Maths.
Where the techniques of Maths
are explained in simple terms.

Trigonometric functions - Integration - Applications finding areas.
Test Yourself 2.


 

Solve the following problems as indicated:
Area -
1 curve		 1.  
  3. A normal is drawn to the curve y = sin x at .

The normal cuts the x-axis at Q.

(i) Show that the equation of the normal is .

(ii) Find the coordinates of Q.

(iii) On a diagram, shade the region bounded by the line , the normal at P and the x-axis.

(iv) Find the area of the shaded region.

  
     
Area -
2 curves

7.

The diagram shows parts of the curves
y = sin x and y = cos x.

(i) Find the x coordinates of the two points A and B.

(iii) Calculate the area of the shaded region.

Answer.(i) A is (π/4, 1/√2)
B is (π, 0)
(ii) Area = √2 + 1 u2.