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find the definite integral between limits 1 and 2 of (4x^3+1)/(x^4+x) with respect to x

first notice the integral is in the form f'(x)/f(x), and indefinite integrals of this form are ln|f(x)|+c. therefore the integral is [ln|x 4 +x|] between limits 1 and 2. subbing in limits gives ln|2 4 +2|-ln...
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Answered by Tutor22645 D. • Maths tutor
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Can you solve (2x-4)(x+1)=0?

All we need to do here is find the values of x that make each bracket zero.So2x-4=02x=4x=2andx+1=0x=-1
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Answered by Samuel I. • Maths tutor
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Form the differential equation representing the family of curves x = my , where, m is arbitrary constant.

Differentiating the above equation with respet to y:dx/dy = m;Substituting the value of m in the given form:x = (dx/dy) y i.e. the solution is(dx/dy) y - x = 0
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Answered by Piyush S. • Maths tutor
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In triangle ABC, right angled at B, AB = 3 cm and AC = 6 cm. Determine angle BAC and angle ACB.

Using the trignometric principles,sin (ACB) = AB/AC = 3/6 = 1/2Thus, angle ACB = 30 degreesand angle BAC = 90 - angle ACB = 60 degrees
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Answered by Piyush S. • Maths tutor
16601 Views

Find the zeroes of the quadratic polynomial x^2 + 8x + 15.

x 2 +8x+15 = (x+3)(x+5)So, the value of x 2 +8x+15 is zero when x 2 +8x+15 = 0 i.e. x = -3 or x = -5.
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Answered by Piyush S. • Maths tutor
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