His question is designed to be answered without a calculator. Two students wrote antiderivative formulas for k sin (kx), where k > 1. Student 1: Integral of (k sin (k x) ) d x = k squared cosine (k x) + C Student 2: Integral of (k sine (k x) ) d x = negative cosine (k x) + C Which student, if any, wrote a correct antiderivative formula? Student 1 only Student 2 only both Student 1 and Student 2 neither Student 1 nor Student 2

Student 2 only

Step-by-step explanation:

Given that:

The written antiderivatives formulas by the students for k sin (kx), where  k > 1 are:

Student 1 :

Student 2:

The student that wrote the correct anti-derivate formula is Student 2 only.

This is because:

Suppose:

where; k > 1

This implies that:

  because

here;

C = constant of the integration

∴

I = - cos (kx) + C  which aligns with the answer given by student 2 only.

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.