Integration of a Determinant
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Q.
Let f(x)=∣∣
∣
∣∣a(x)b(x)c(x)m(x)n(x)l(x)g(x)h(x)k(x)∣∣
∣
∣∣ then
∫a0f(x) is∣∣
∣
∣∣∫a0a(x)∫a0b(x)∫a0c(x)∫a0m(x)∫a0n(x)∫a0l(x)∫a0g(x)∫a0h(x)∫a0k(x)∣∣
∣
∣∣
False
True
Q. If f(x)=⎧⎨⎩mx2+n, x<0nx+m, 0≤x≤1nx3+m, x>1. For what integers m and n does limx→0f(x) and limx→1f(x) exist?
Q. If f(x)=∣∣
∣∣12x3x23a27139∣∣
∣∣ and ∫30f(x)dx=0, then a is equal to
- 3
- 6
- 9
- any real number