g(x)=∣∣
∣
∣∣1+p2x(1+q2)x(1+r2)x(1+p2)x1+q2x(1+r2)x(1+p2)x(1+q2)x1+r2x∣∣
∣
∣∣
Applying C1→C1+C2+C3
g(x)=∣∣
∣
∣∣1(1+q2)x(1+r2)x11+q2x(1+r2)x1(1+q2)x1+r2x∣∣
∣
∣∣ (∵p2+q2+r2=−2)
Applying R1→R1−R3, R2→R2−R3
g(x)=∣∣
∣
∣∣00x−10−(x−1)(x−1)1(1+q2)x1+r2x∣∣
∣
∣∣
⇒g(x)=(x−1)2 ∀ x∈R
So, 4∫1 (x−1)2 dx=13[(x−1)3]41=9