If _0^1 (4x^3 + 3x^2 + 2x + k)dx = 0, then the value of 'k' is Option 1: 1 Option 2: -1 Option 3: 3 Option 4: -3

Answer: -3. Solution: _0^1(4x^3+3x^2+2x+k)dx=[x^4+x^3+x^2+kx]_0^1=1+1+1+k=3+k. Setting 3+k=0 gives k=-3.

Calculus

Integrals

Easy

common

If $\int_0^1 (4x^3 + 3x^2 + 2x + k)dx = 0$ , then the value of 'k' is

-1

-3

✅ Correct Option: 4

$\int_0^1(4x^3+3x^2+2x+k)dx=[x^4+x^3+x^2+kx]_0^1=1+1+1+k=3+k$ .

Setting $3+k=0$ gives $k=-3$ .

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