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{:[H(x)=3x^(2)-6],[h(x)=H^(')(x)],[int_(-1)^(0)h(x)dx=]:}

H(x)=3x2−6h(x)=H′(x)∫−10h(x)dx= \begin{array}{l}H(x)=3 x^{2}-6 \\ h(x)=H^{\prime}(x) \\ \int_{-1}^{0} h(x) d x=\end{array}

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Find derivatives of sine and cosine functionsright chevron icon

Full solution

Q. H(x)=3x2−6h(x)=H′(x)∫−10h(x)dx= \begin{array}{l}H(x)=3 x^{2}-6 \\ h(x)=H^{\prime}(x) \\ \int_{-1}^{0} h(x) d x=\end{array}
  1. Find derivative of H(x)H(x): First, find the derivative of H(x)H(x) to get h(x)h(x).\newlineh(x)=ddx(3x2−6)h(x) = \frac{d}{dx}(3x^2 - 6)\newlineh(x)=6xh(x) = 6x
  2. Integrate h(x)h(x): Now, integrate h(x)h(x) from −1-1 to 00.∫−106x dx\int_{-1}^{0} 6x \, dx
  3. Calculate the integral: Calculate the integral. \newline=∫−103x2dx= \int_{-1}^{0} 3x^2 dx
  4. Evaluate at bounds: Evaluate the integral at the bounds.\newline=(3(0)2)−(3(−1)2)= (3(0)^2) - (3(-1)^2)\newline=0−3= 0 - 3\newline=−3= -3

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