If -1k2 x-3 dx -12- then k -A- -2 and 5B- 5- 2D- -5

The correct option is A 2 and 5∫_1^k(2x 3)dx=12 ⇒[x^2 3x]_1^k=12 ⇒ k^2 3k 1+3=12 ⇒ k^2 3k 10=0 nbsp; ⇒ (k 5)(k+2)=0 ⇒ k=5, 2 ...

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Standard XII

Mathematics

Proof by mathematical induction

If ∫1k2 x-3 d...

Question

If $k \int 1 (2 x - 3) d x = 12$ , then $k =$ ____

- 2

and

5

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Solution

The correct option is A $- 2$ and $5$
$k \int 1 (2 x - 3) d x = 12$
$\Rightarrow {[x^{2} - 3 x]}_{1}^{2} = 12$
$\Rightarrow k^{2} - 3 k - 1 + 3 = 12$
$\Rightarrow k^{2} - 3 k - 10 = 0$
$\Rightarrow (k - 5) (k + 2) = 0$
$\Rightarrow k = 5, - 2$

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If k∫1(2x−3)dx=12, then k=____

The correct option is A −2 and 5k∫1(2x−3)dx=12 ⇒[x2−3x]k1=12 ⇒k2−3k−1+3=12 ⇒k2−3k−10=0 ⇒(k−5)(k+2)=0 ⇒k=5,−2

If $k \int 1 (2 x - 3) d x = 12$ , then $k =$ ____

The correct option is A $- 2$ and $5$
$k \int 1 (2 x - 3) d x = 12$
$\Rightarrow {[x^{2} - 3 x]}_{1}^{2} = 12$
$\Rightarrow k^{2} - 3 k - 1 + 3 = 12$
$\Rightarrow k^{2} - 3 k - 10 = 0$
$\Rightarrow (k - 5) (k + 2) = 0$
$\Rightarrow k = 5, - 2$