Question

The area of the region bounded by curves \(y = sinx,y = cosx\) and the lines \(x = 0\), \(x = \frac{π}{4}\) is

• A. \(2\sqrt{2}-1\)
• B. \(\sqrt{2}-1\)
• C. \(2-\sqrt{2}\)
• D. \(\frac{1-\sqrt{2}}{2}\)

Hint:

Clear the fractional power by cubing before reading the degree.

Answer 1

The Correct Option is B

Step 1: Order:
The highest derivative present is \(\frac{d^3y}{dx^3}\), so the order is 3.

Step 2: Remove the fractional power:
Rewrite as \(\left(\frac{d^3y}{dx^3}\right)^{7/3} = 3 - \left(\frac{dy}{dx}\right)^5\). Cube both sides:
\[ \left(\frac{d^3y}{dx^3}\right)^7 = \left[3 - \left(\frac{dy}{dx}\right)^5\right]^3 \]

Step 3: Degree:
The equation is now a polynomial in the derivatives, and the highest derivative \(\frac{d^3y}{dx^3}\) has power 7. So the degree is 7.

Final Answer:
Order 3 and degree 7, option (A). \[ \boxed{3,\ 7} \]